It does when your Party are the FPTP!
The one strong point of this system is whoever achieves that objective gets first crack at forming a Government and if they have the overall working majority they can start to implement their manifesto. Power is truly in the hands of the people or if you prefer 'democracy'.... any other system that relies on parties 'scratching around' to reach agreement with others tends to mean that deals are done behind closed doors, or as they use to say in 'smoke-filled rooms'. Where the public only gets to know the final outcome and everyone taking part is 'whipped' into secrecy.
Proportional representation sounds a fairer bet, but in its purest form, would mean umpteen smaller parties all trumpeting their own requirements,' talk-talk,' beer and sandwiches all round and gatherings which would make the recent party-gate events look mild and there would still be a good chance that nothing ever got done.
Its true that under FPTP, having 80+ seat majorities are also to be decried. Thankfully Boris didn't get to implement the worse excesses of his overwhelming margin of power, but only because the red-wall Tory MP's had one eye on the next GE.
To exercise power you have to win it, to win it you have to 'follow the Herd' otherwise they will leave you behind. Brexit has given many a taste for 'exercising their muscles' not because of its objectives, but how it operated, i.e. a massive pressure group made up mostly by people who felt (albeit for different reasons) completely p***ed-off they threatened to apply political 'weight' at a single point 'weak point' (in this case) the heart of the Tory party who realised they could be obliterated if they didn't grab the Brexit mantle from Farage and Co. Opportunists such as Farage and Boris read these signs ages before the rest of us.
At last Keir Starmer seems to realise that he cannot afford to let it happen again and is waking up to the necessity of''walking the line'.
I have to smile a little at this discussion about how a PR-based system would work, as if conjecture based on personal experience of committee work and general speculation was the only way to answer that question. Most democracies have PR, so possibly one could judge how a PR-based system works on the basis of their experience instead?
It is a question of some complexity that a lot of things play into though - it's how the different elements of a country's whole political culture and institutional and legal setup come together that gives us the observable result, and it's hard to pick out precisely how the mode of representation plays into it. So, to some extent what works in a certain way in one country might not work in the same way in another. But I do think some valid general points can be made.
FPTP and PR causes political parties to become very different things. In a PR system, parties tend to become highly representational tribes - built around a shared general political vision, or sometimes other things (regional or ethnic identity, defining single issues etc). Generally speaking, if there's a sizeable group or constituency of opinion that isn't well reflected by one of the existing parties, this will tend to generate a new party. This means that political parties tend to be genuine communities of shared views or shared interests in a way that is not the case in a FPTP system - if there's too much tension within an existing party, one wing will tend to peel off.
With FPTP, the threshold of meaningful success for a new party is so high that this generally does not happen, because there's not much point. Instead, you get huge parties that really are not communities of shared belief in any meaningful sense, but rather either organisational machines built to pursue power on the basis of politics that are really very vague and shifting, or broad church confederacies of various groups that really do not agree on enough things to co-exist constructively, but who have nowhere else to go. In both cases, where parties stand politically tends to reflect which particular faction is currently on top, rather than any broader consensus in the party (let alone its voters).
Generally speaking, a FPTP system tends to foster a polarised and oppositional political culture, whereas PR tends to foster a political culture much more oriented towards co-operation and consensus. It's not straightforward, and is affected by lots of things: For instance, other traits of the US system has traditionally stimulated cross-party co-operation despite a FPTP system, though this is by now showing signs of breaking down. Whereas France has a highly polarised political tradition despite having at least partially a PR system (and it was arguably even more so back when they had a much clearer PR system than they have now).
It's an easy temptation to think that the advantage of FPTP is that it results in more efficient governments that can get things done more easily, while the advantage of PR is, more nebulously, that views are represented more fairly. But this I would argue is not necessarily so. Because societies really aren't built and shaped by individual decisions, or in four years. If you want to build and shape something, and not just end up with whatever's the net result of a jumble of disjointed and, over time, contradictory decisions, it requires a consistent sense of general direction and design over decades. This requires that there is some degree of shared thinking among the major political parties, and also that there is an ability to sit down and agree on a long-term arrangement occasionally. Certain things - pension or tax reform, defence investment, large infrastructure programs - simply cannot be solved well on the basis on one group of people doing their thing for a few years and then another group of people doing a different thing for a few years. Most places, you get broad consensus agreements in place for such things, but that simply does not happen in the UK. And if you can't do that when you really need to, it hurts you.
My point here is that every democratic system actually needs to be able to do cross-party policy making and consensus-based politics, at least occasionally. A system that can't, or doesn't even try to, is simply dysfunctional. It will be faced with problems it can't solve well, or at all. Given that, is it really an efficiency advantage to have an electoral system that allows the ruling party to just ignore cross-party co-operation, in many cases? At the very least, that means that when you do end up with a situation that requires this, the system isn't really equipped to handle it. In a PR system, this is a matter of day-to-day necessity, and the whole apparatus of government evolves around that. Clearly, it is quite feasible to govern well and solve problems efficiently on that basis. Indeed, if you look around the Western world and ask yourself who seems to have gotten things more or less right and have a political system few regards as being in a state of crisis, most of those you'd name have PR. On the other hand, if you're picking the ones that are obviously in deep trouble, a couple of big FPTP countries are well ahead in that queue.
I'd question your use of the term "back-room" deals here. What does that mean, exactly? If we're talking about shady dealings of various kinds that does not stand the light of day, I really do not think a FPTP system make those less likely or common - if anything, the opposite. If you're talking about agreements between political parties, then I think your terminology is weird, and also that there's little reason to think there is less of this in an FPTP system.