I think there are a few separate issues here that it's worth clearly separating, because they seem conflated:
1) Local business vs. non-local/international business
You seem to have a clear preference for local businessmen owning the club. But football is now an international game, so local/regional owners are going to be unbelievably rare. Even if you define local as "UK", which I think is broader than you intended, there are very few Premier League teams currently owned by British businesspeople/businesses, let alone those whose wealth is actually maintained within the UK. It's just not realistic anymore, much as I miss Franny Lee.
2) Business vs. states/oligarchs
I agree with you that it doesn't seem right for states or oligarchs (using your term) to own or own states in clubs. This could be on two levels, which again can be separated: a) states/oligarchs have disproportionately more money; b) states/oligarchs may have accrued their money in dubious ways, and states in particular may pursue policies (e.g. human rights, etc.) that we consider unpalatable. Point a) probably leads us to FFP so no need to debate. The problem with b) is in enforcement on many levels: How would you define an oligarch? How do you determine "dubious" sources of income? How would you determine which policies are unpalatable? I'll also mention here, because it's frequently written in the media and on here, that Manchester City are not state-owned. At the time of the take over, we were wholly bought by ADUG, which is a private equity firm wholly owned by Sheikh Mansour (in 2015 CMC, a Chinese consortium took 13% of ADUG's share). While he holds a position in the UAE government and is a member of the royal family, Sheikh Mansour's ownership of ADUG is legally private. Even if you may consider it to be a technical distinction, it is a distinction that would have to be enforced somehow -- we've already seen disagreement today on the forum on whether the proposed new Newcastle owner is a senior enough royal to meet some sort of state-owned definition. This is different to PSG, for example, which is legally state-owned as ownership is by the Qatar Sports Investment, which is a subsidiary of state-owned QIA.
3) Ownership vs. commercial/sponsorship by states/state owned companies
The other point to consider on part b) of the states/oligarchs discussion of above, is that if the unpalatable policies pursued by these states is truly a serious consideration, and I agree it is, then I think we should consider banning both ownership and sponsorship of football clubs by unpalatable states/state-owned companies. City obviously gets criticised for our UAE connections, and you see phrases like blood money. No-one really has a problem with Emirates, a UAE state-owned company sponsoring Arsenal though. Clearly there is distinction, but does that distinction really matter to a labourer or dissident in the UAE whose human rights have been stripped? You can extend this argument to other state-owned airlines like Qatar Airways (Roma, Bayern, FIFA) and other companies like Gazprom from Russia (Chelsea, Barcelona, Champions League). I think you should have to ban unpalatable money irrespective of how it is provided, but again, the challenge will be determining which states/state owned companies we find unpalatable.
I guess the point I'm making is that it's actually quite difficult to develop policies around who we do and do not want owning our football clubs. There have been plenty of terrible club owners, irrespective of whether they're local or international, or whether they use dubious/state money or don't. One part of the issue related to disproportionate investment is already covered (imperfectly) by FFP, but the Fit and Proper Person's test is totally unfit for purpose in this regard.