I've noticed a lot of people struggling to get when they should use the supine I or the present infinitive, but it's easy to tell apart with the following questions:
- Infinitive - "what do you [head verb]?"
- Supine - "why do you [head verb]?"
So for example, "I want to sleep":
- What do you want? To sleep. - OK, infinitive: dormire uolo.
- ~~Why do you want?~~ - this sound like rubbish so no supine here.
Doing the same with "I go to sleep":
- ~~What do you go?~~ - this sounds like rubbish, so the infinitive doesn't work here.
- Why do you go? - to sleep - OK, supine time: dormitum eo.
The key here is that the infinitive - unlike the supine - is simply filling as the direct object of another verb. You could replace it with a noun in the accusative, and the other verb would be happy; in the meantime the supine is doing something else, as the text says it's all about "purpose".
Romance speakers: be warned that Classical Latin barely used verbs of movement as auxiliaries, that's mostly an innovation from Late Latin. That's why we spam infinitives where Classical would use the supine instead.