"We thought after we made it there the enemy would flee, but it didn't turn out that way."

I'm not sure it was the US's idea. Same as with Bakhmut i think they were telling Ukraine to stop throwing away resources on other fronts and just put everything they have into attacking in Zaporozhye to cut the land bridge. (Which is also bad advice since that was the most highly fortified and mined section of the front as we saw, and concentrating assets like that just makes them easier targets for Russian artillery, but that's a whole other discussion.)

I think the Dnieper crossing gambit was a British idea, they are enamored with these sorts of flashy special forces operations whereas the Americans favor simpler brute force solutions (usually involving just bombing everything from the air, something which cannot be done against Russian AD).