You can treat wounds once per day (or twice, of you consider cleaning and dressing to be two attempts). However, once a treatment attempt has resulted in the best treatment state you can achieve, further treatments can at best succeed in not making it worse, and often result in a worse state, so the only benefit from further treatment is meta gaming by training the Physician skill.
Wounds can kill you through bleeding, but if that is staunched (through treatment or on its own) it will eventually heal completely on its own. Poison can kill you, but I don't believe disease can, currently. If you've suffered severe blood loss treatment can be dangerous, as it can reopen the wound to cause it to start to bleed again.
The current wound model is definitely fairly basic, and I believe the dev page mentions expansions to it, at least in the form of scars.
The most basic improvement to the current model would probably be to let the effects of treatment fade back to a basic "natural" level so you're encouraged (beyond training) to clean and re-dress wounds regularly. From there it could expand to include worsening effects and negative effects from the lack of treatment.