If it's possible to max all stats, it's not min-maxing, it's just maxing. Min-maxing is making the most of your limited points.
The player is directed to New Texas on Day 2. 10K for a Lifetime membership at the Gym is expensive for the first planet or two, but peanuts later.
The unintuitive things about the Gym, in my opinion:
1. It's better to eat at the Bucking Bronco instead of going all the way back to the Ship to sleep.
2. You should Train first, then spend Stat points. In fact, it's possible to bank enough you don't have to Train later.
3. You shouldn't put your Affinity in a stat you plan on raising primarily with Stat points.
I think the developers see Slow Stat Gain as a bonus, not something they expect the player to do.
I know all of that. Please don't be pedantic with 'min-maxing'. Raising your stats by grinding a lot in the early levels, so that you can cruise on by without needing to train at higher levels; effectively rationing your limited amount of free level-up attribute points? That's literally min-maxing ('...
making the most of your limited points') as you defined it, and can result in max stats for the player.
Again, New Texas just isn't a probe location. There aren't any other gyms in the entire game (as opposed to how many different transformative or weapon vendors there are). Heck, there are more places to purchase ships and ship upgrades. You can't even do something as reasonable as purchase an 'at home' gym and slap it inside your ship next to the Dong Designer (which ironically enough, appears on Tarkus with the upgrade is on Zheng Shi, both probe locations).
The current system is janky, inconsistent, and unintuitive. Wanting to get the most out of it requires consulting outside resources like the wiki. What raises your stats is largely arbitrary, and I don't think anyone can honestly argue that is not the case. I think the system as it stands now is a detriment to the current player experience, and would greatly benefit from being expanded with a consistent logic so that new players could actual intuit how the system works from within the game. Ideally a complete overhaul into a usage based system would be the most intuitive and straightforward system from a player's perspective, but I get that might require a more bottom-up rebalance of content and mechanics (e.g. percentile based stat checks).
The game isn't just an erotic text adventure. They put a full-blown RPG and combat system in here. If you're going to put in a progression system, why not put in a good one? Stats can already be raised outside of leveling up; that Pandora's Box has already been opened. So why not make it straightforward, easier to understand, more intuitive, and less grindy to do so? Again, even if a new system or overhaul is over-tuned and makes stat gains far more plentiful and easier to get, you can also adjust the stat points on level up to smooth out the progression speed.
Any game mechanic worth doing, is worth doing well.