Panther was a case of trying to do it all with technology that wasn't there yet and far, far too many engineering shortcuts in the drivetrain.
It had a totally adequate main gun, when the 88s were really overkill against anything up to an IS-2. But it also had a very traditional 3-2-1 armour arrangement.
It influenced post-war design most in the sense of; "What if we could do that, but actually make it work?" That thinking got really pinched off with proto-MBT concepts, which was a short-cut to doing even more by making trade-offs that were unthinkable ten years earlier.
What Panther really did most was in the Main gun; which was copied by the French and used with an autoloader in the AMX-13 and ironically in the Israeli M50 Super-Shermans hand-loaded. It was a real medium-tank gun, which when copied and refined a bit was ideal for tanks of it's class.
The class issue is confusing because when discussing tanks; you need to look at design and not designation (I feel i am being condescending here and I appologize profusely); because designations change constantly. The same Pershings were designated as mediums, heavies and then mediums again. The M46 was considered a tank destroyer briefly for truely obscure reasons, despite only having a different turret and the M47 was almost the exact same tank with a new turret again and called an MBT when it entered service.
Panther's problems were probably fixable, but not in a setting where you still have PzIIIs rolling off the lines in mid-44 and PzIVs still being refined in 1945; it's too much energy wasted on divergent lines. A recurring theme for WWII is no-one being willing to gamble enough on production to slow things down to try and come up with something better or try to really switch over fully to a new type of vehicle. The Germans wasted vast resources of all kinds producing and developing and CONTINUING to develop so many different kinds of fighting vehicles. Common sense ideas like going to the hybrid PzIII/IV chassis as seen in Hummel and Nashorn for ALL support vehicles never got off the ground. Going to King Tiger running gear and new transmission solved most of the Panther's remaining automotive issues; but that didn't happen until early 45. The main gun was still totally fine for anything but the IS right through until 1973, when the Israelis found that they really had kept the last of the M50s around too long; thus they all went to Chile and Lebanon after that, while the IDF retained the 105-armed M51s in reserve service for a while longer.
The problem for the Germans was that when you're drowning in T-34s, you don't want to shut down your Panzer III and IV lines for a few months to a year for more Panthers (that aren't there yet, developmentally) you want more tanks you know work and you want them right now. Likewise; people are screaming for more Panthers, Tigers, ect; so any issues they have need to be fixed on the production line; which leads to increased variation (bad) and the fixes may not stick (Worse).
It's easy to forget that real nations aren't run by omniscient power-gamers, willing to gamble big and then reload the game if they lose. Maybe the solution was to pour everything into STUGs/JPzIV in 1941? But who was really going to make that call?