If you’re burning hydrogen to power a rocket, you don’t get to keep the exhaust. If, on the other hand, you use hydrogen and oxygen to power a fuel cell, keep the water, and use the power output to power an ion thruster or similar device, I suspect you end up with worse overall results than simply using a rocket and carrying some water.

Apollo used fuel cells to good effect. Their constraints lined up perfectly - they already needed oxygen tanks, and a supply of water, and they didn't have li-ion batteries back then either. Also, the weight cost of the fuel cells themselves amortizes nicely when you need power for an entire week - and hydrogen is light. And once it had been used, the water was flushed, saving further weight. The big downside to batteries is they weigh the same empty and full.