Is the sentence "Ik kom eten" in some way connected to the sentences "Ik zit te eten", "Ik loop te eten" etc., in the sense that eten is the important part and kommen/zitten/lopen are auxiliary verbs?
Are this kind of "I kom ..." sentences also mainly(?) used in informal situations like the other ones I just mentioned?
I'm not a native speaker, but the way I see it, in Ik kom eten, kom is acting as a modal verb, and thus it's the only verb that is conjugated.
Now, in the case of the second verb, eten, you cannot add te before it because with modal verbs you need to use a bare infinitive (i.e., without te) and not a full infinitive (that is, the one with te before the infinitive verb).
Hope this helps :)