They would be waiting on Chakotay. He'll be the one telling the cadets, "Do this" and "Do that".
They left Tars Lamora to ESCAPE from bondage. Tying themselves to Chakotay would means throwing themselves back into it.
Dal has just had a taste of power. I seriously doubt he's just going to casually stand aside.
The fact that the creator of Prodigy said 3 new character will join the Protostar (a SF Commander, a doctor and a SF cadet) points to the idea that Dal won't have a choice in the matter of whether or not he wants to be a cadet in training.
They left Tars Lamora to escape slavery and oppression. Hierarchy exists on a SF ship... and Dal won't be able to overrule a fully commissioned SF Commander.
Plus, Dal expects the other kids to follow his orders as a self-proclaimed captain? That's not bondage? He's already encountering resistance to that.
The kids (maybe not Dal specifically) would likely be more comfortable having someone who KNOWS what they're doing in charge of the Protostar.
Dal can develop his leadership skills in the interim
Protostar has a ship replicator. Chakotay might've just made himself a small ship, scuttled Protostar, and flown off to God-knows-where.
Could have indeed.
But that still leaves the option that he could be found at some point and re-assume temporary command of the Protostar until they return him to UFP.