我来 uses 来 as a grammatical 'come forward to do' marker — not physical motion. Pattern: 我来 + verb ('I'll do the verbing') or just 我来 on its own ('I'll take it'). Very common in group settings to claim a task.
usage
Volunteering flavor — warm, helpful. Compare with 交给我 (stronger: 'leave it to me') and 包在我身上 (confident: 'I've got this covered').
