It's a cop out-to say British Asian parents only want their kids to become doctors and lawyers. The same stereotype is supposedly true for British African parents, but that hasn't prevented a fantastic uptake from that part of society. It's also particularly nonsensical when you look at the levels of unemployment and poverty found in some British Asian communities. Of course those families want their kids to be playing football instead of picking up the dole or driving taxis or working in a kebab shop.
There are around 5 million British Asian people in this country. Whether or not you believe the factors listed in the rest of the thread, their representation in English football should still be greater that what it is. At the very least, you can accept the population numbers are available and so is the level of enthusiasm for the sport. From there, it doesn't take a big leap to figure out that a not-insignificant number of kids must also possess the requisite ability to make it (by simple law of averages, if nothing else).
If you want to play the numbers game, we can also do that. Out of 7% of the UK, let's say Asian kids and families are only half as interested in football as everyone else (I don't think that's anywhere close to reality, but whatever). That would still mean we should expect 3.5% of homegrown professionals to come from their background. We could go further and believe British Asians are only half as athletic as everyone else (a guesstimate not borne out by participation levels in other sports, but again whatever). The proportion would still be expected to be around 1.75%, and that's as a worst case. Instead, we're practically seeing 0%. The problem is so absolute and so irreconcilable with any sober analysis that it points to something deeper and more institutional.
You're making a very large assumption that the rate of people with the potential to play football at an elite-level is consistent across all ethnicities. However it's clearly not true given the disproportionate number of players with African or Caribbean heritage in the English national team. If South Asians are not as athletic as other ethnicities, it would be unlikely realised as a binary factor of half being unable to make it but the other half remaining in with a chance, it's far more realistic that the factors inhibiting athleticism, such as genetics, diet or culture, would be dispersed across the entire group. As such, even the most athletic South Asians would not perform favourably compared with the most athletic from other ethnicities.
Every time I've heard this subject matter discussed there has always been the same underlying error of assuming that given enough participation the rates of representation from all ethnicities should normalise to their population rates. This ignores the reality of how extremely rare it is have the talent to be an elite footballer and also the luck to fulfil that potential. The footballing ability of the average person from each ethnicity is likely to be similar but professional footballers aren't average, they are from the extreme end of the distribution across multiple factors. Marginal advantages or disadvantages are amplified within this group since any mediocre performers across any relevant factor have been filtered out. You are comparing the best and selecting from them. To illustrate the point with a simple example imagine we had a country with a population of 100,000 people and two ethnicities, 10,000 of A and 90,000 of B. The overall rate of producing footballers is extremely rare at just 0.03% which if it was consistent across A and B would produce 3 footballers in A and 27 in B and the population rates would be preserved. But if A had some minor advantage, say a higher prevalence of very high-level co-ordination, resulting in their chances marginally improving to 0.1% then the rate of B would be 0.0222% producing 10 and 20 footballers respectively. The chances of any person from A or B becoming a footballer, without knowing any prior information about them, is still extremely rare but the rates at which each group does produce them is disproportionate with A over-represented by more than a factor of 3 because of a minor improvement in their rate of producing footballers.
What is also worth taking into consideration is that there is a natural limit to the number of footballers there can ever be at one time. The 20 Premier League clubs can only have 25 players in their squad. This inevitably creates a non-static threshold to becoming a Premier League footballer. Unlike most other jobs, where the number of opportunities isn't heavily bounded, the criteria to qualify remains stable over time. The requirements to be a doctor, lawyer, electrician or accountant have not changed rapidly over the last few decades since the amount of work and jobs has risen in tandem. But imagine a world there are initially 500 electricians and only ever enough work for 500 yet over time almost everyone wanted to be one, it would create a competition of increasing intensity amongst each other pushing the qualifying criteria further away from first the ordinary, then the good, then the great to leave only the excellent with a realistic chance of meeting it. That has been the case over the last few decades with football, it is clearly evident when comparing the fitness and athleticism of players today to those in the 90s. Football clubs, schools and parents are having increased involvement in getting children on the path to being a professional footballer at an earlier age, which is pushing the threshold towards those with detectable advantages at an early-age, likely to be hereditary, that also grow up within a household that emphasises football as a career. I suspect there aren't that many South Asians of that type.
Selecting for small groups based on extreme criteria will lead to noticeable discrepancies compared to rates in the wider population since marginal advantages between sub-groups make a difference. It is not a phenomenon exclusive to football, it's apparent in almost every other sport, applications for the world's best Universities, and high-paying prestigious careers. Therefore the lack of South Asians in professional football isn't that shocking. Their conspicuous absence might be but the main population centres of South Asians (India, Pakistan, Bangladesh etc.) don't take football seriously enough for any rare potential to be realised. What I would then ask is should it be seen as a problem? Football isn't a perfect meritocracy but it's closer to it than almost everything else. The form of the product itself informs an objective view over who is capable that can't be deduced for most other occupations. I would argue that the few thousand British professional footballers are close to being the best few thousand at kicking a ball around in the UK and had been even before they turned professional. I'm South Asian myself and I struggle to understand what the motivating issue is for the ordinary South Asian to not have anyone of their resemblance playing football professionally.
There could be a case to be made for bias against South Asians when they are being passed over for trials or training due to clubs, or scouts, wanting to put their efforts into known quantities leading to a negative feedback loop. A club might be presented with two players of equal talent, with only one of the being South Asian, but only have the funds to train one and choose the non-South Asian since they are seen as having a greater chance of making it based on the demographics of current footballers thus further compounding the problem. I'd argue it's a rational decision by the club, from their point of view, to focus their resources into those they feel less uncertainty around. I'm not saying their view is correct, their view of the future trajectories of these players might be unfounded, however it is the one minimising risk based on experience. The even stronger counter-argument is that Premier League clubs don't work under such constraints since an academy player is magnitudes cheaper to train than buying one, so it's in their best interests to find any train any player they thought had potential. The fact that not many South Asian players are in Premier League academies suggests that few thousand best at kicking a ball around in the UK doesn't consist of many South Asians at all.
