One issue with the TDT framework for ordinary decisions/actions is that “every time you take an action (or don’t), you become more the kind of person who takes (or doesn’t take) that action” can put a huge weight on every action in a way that can become psychologically crushing. Decisions become agonizingly hard; one suboptimal action can cause a spiral of shame and discouragement and pessimism that makes it harder to do things in the future because you’ve already updated so much towards you being incapable of doing things (in addition to just being extremely unpleasant). If not going to the gym is an indication that you are the kind of person who doesn’t go to the gym, then if one time you fail to go to the gym you think of yourself even more as the kind of person who doesn’t go to the gym, which can become part of your identity/how you think of yourself, which can make it even harder to change (and since many people imbue going to the gym with moral valence, this can cash out to “I am a bad/useless person”).
A lot of people need to learn the opposite of TDT first, if they’re stuck in that kind of spiral. One instance of going to the gym is one instance of going to the gym, missing this one time doesn’t mean you’re doomed to never make it to the gym again, you are still a person with potential even if you didn’t use this one afternoon in a particularly effective way. (This is basically unlearning the all-or-nothing thinking that is often a big part of depression reasoning.)
At the same time, yes, the things you say here are true; and truly unlearning all-or-nothing thinking means learning this while also not imbuing your actions with more power than they actually have. What you do today doesn’t determine what you will do for all time going forward, but it does have some effect on your future actions, and as such what you do today is one possible intervention point for changing what your future life will look like.
I guess the only change I’d make to how people talk about TDT for humans is to not make claims that are stronger than reality. “If you make this decision today, you will also make the same decision in all analogous situations” is not actually literally true. “If you make this decision today, you make it more likely that you will also make the same decision in future analogous situations” is truer and less fatalistic.