Relative fan base size is hardly relevant in the PL where gate and merchandising income maybe adds around 10% of total income for most clubs. Look at the massive disparity in ST prices across PL clubs. Owners don't deliberately keep prices down for the benefit of the fans, it is to maximise gate revenue over the season by getting more punters in. Unless clubs have serial big time successes on the pitch (like the so called top 6), there are simply not enough fans who want to pay the high price for access. Clubs like Derby, Leeds, Nottingham Forest are only attractive if they can be bought very cheaply, have a decent stadium and there is a good prospect of getting into the PL and staying there with half decent football.
Sunderland are doing the League One experience for the second time in recent history, despite having high gate turnouts and ST sales. Ellis Short, a US billionaire took a bath on his investment there, as after a few years of clinging onto PL survival, they slipped and plunged. Most of these investors do not care about football, they care about making money, so very soon stop putting money into the club. They all think they will use the "develop young talent and sell it high" approach, which even Southampton have found difficult to produce in recent years. Short made most of his money by trading distressed debt, a very ugly industry. I believe the prospective Southampton buyer has been in that arena too, though it has largely been billed as "Capital Investment Consulting".