Talking of purchasing outright, that has some clear advantages.
Unless you are in the extremely unusual position of having a self fly hire operator with modern and new planes in your airfield, a purchase is the only way to get a plane which isn't a decrepit piece of junk. Even if the pilot is an aviation anorak and thinks that a 1970 PA28 is really good, most ordinary people won't touch it and this will show up in who will be a willing passenger
It's the only way to get unrestricted availability.
It's the only way to get maintenance to one's own standard.
For most people, it will be the only way to get an aircraft which is IFR legal in CAS.
The marginal cost (per hour airborne time) of a brand new £200k aircraft is less than the cost of hiring an old C152 - so it's a lot cheaper to keep current.
If flying more than say 200hrs/year, it is cheaper to buy than to rent something properly maintained, overall. I say "properly maintained" because the economics of most flying schools rely on non-maintenance of of anything which isn't essential, so the aircraft slowly falls apart.