You don't see Driving Schools offering lessons in 1960's cars so why does aviation training continue to think it is acceptable/desireable to use 1960' aeroplanes?
Driving schools dont use 1960's cars because they barely pass MOT's, are not very comfortable (no driving schools is going to be using a Jag XJS), cannot have dual controls, are not very economical, probably have a 'choke' which is not a term referred to in any driving school manual, and probably dont start in cold temperatures.
Now, you could say a lot of that applies to a flying school PA28 / Cessna (especially the bit about "dont start in cold temperatures"), but the reality is that except the glass cockpit types, even modern planes are built with the same engines, instrumentation and avionics as the "old" ones. Meaning these old planes meet the requirements of the training manuals (which some will say are WWII training standards, and that might be true) and unless you progress straight onto glass, what you learn on, will be very similar to what you do your flying on post-PPL.