Without wealthy owners bankrolling clubs the costs would be lower as players, staff and the like would not be able to demand such high wages. Pretty much as in the past the more successful clubs would generate more money and thrive thus attracting bigger gates and more revenue and the rest would have to get by on the scraps from the table.
So , yes , professional clubs would still exist without wealthy owners.
The Lansdown situation is an interesting one. If he really wants to sell then the asking price has to be interesting for a buyer which it appears it isn’t. So he drops the price or he leaves Aston Gate in a coffin and his wife or kids ‘profit’ from their inheritance.