TLDR: Give more specifics about your "Balanced Gym" and consider the actual PRO's/CON's of being balanced with real numbers right now your suggestion has no solid argument as to why such a gym is "necessary."
Technically, for balanced the best gym is the going to be the Sports Science Lab. The catch is gimping yourself by not using roughly more than 50 Xanax (which probably defeats the point of being balanced at least competitively in the long run and not something I would recommend if you want to be as strong as possible battle wise).
If you are serious about trying to argue a balanced Gym for Druggies at the very least you should suggest exactly how many gym dot's it will have, what the name is going to be, the cost , and why it should be included in the game when there is already Georges available to you.
Off of that idea, you already can figure out that a balanced gym would have to be designed to be worse than any of the 8 dots, and more expensive with maybe only slightly better gains than Georges (really kind of a waste to code such a thing)
IF you are asking for a balanced gym to be equal to or better than any of the whoring 8 dots or even the sports lab, that is ridiculous and you need a reality check because then You would see absolutely no difference in player stat allocations and really no point to the system.
In practice most who balance start off by whoring one stat or another so in essence they will have access to probably Frontline or Balboas at the very least to help get 2 stats to the stat cap. It would be to your disadvantage to simply raise your stats always balanced from 10 to 50 million in all four stats at the same time.
At the 50m stat cap someone with 2600 Happy,+8% gym gains (5 via steadfast) spending 50 E on training a single stat will get approximately these gains below:
This is roughly a it will take the same amount of time to become balanced as you. (This sort of doesn't apply to those who can afford to take SE's cost effectively, i.e. busting abusers)
Taking the above in mind in my opinion the catch about going balanced is really how much money you can spend on Xanax, Cans, FHC, SE's in comparison to your average drug using player who you want to beat (not really the access to gyms). If you cannot at least match their energy spent on training then basically you are gimping yourself for no reason because your effective total stats wont be enough to counter their whoring and will just get worse as time goes on.
Of course this could all change in the new attack system rolling out so balanced(at lower total stats) could become a lot stronger even without the need for a new gym.
If you want to be lazy like me and go for the Science Lab I unlocked it in about 643 days, without using any can's/fhc, and rather low amount of refills (