A big part of the problem is that Biden is trying to include a number of progressive proposals, such as affordable housing and clean energy. Wouldn't it make more sense to attack this in smaller pieces rather than trying to pass a single, multi-trillian$ bill at once?
No, because things like "affordable housing" and "clean energy" are less popular with people generally than "infrastructure" is.
I put these items in quotes because the actual policy specifics matter less than what these words mean in the minds of voters.
Your average voter is likely going to be in favor of the government spending money on infrastructure, regardless of their party affiliation, because there is a bipartisan sense that spending money on infrastructure is part of what the government is supposed to do, and it is good for the economy for the government to do it at the right times. Things like affordable housing and clean energy are not similarly popular, there's a pretty stark opinion divide along party lines about whether these things are things the government should do at all, as well as what priority they should have given other concerns that the government needs to address.
Given that, and the current divided makeup of Congress which makes passing partisan bills into law very difficult, the approach of having separate bills to address progressive policy priorities is likely to fail to result in those policies being implemented.
Even though it would be more rational to create separate bills from the point of view of having coherent policy, that would result in progressives getting next to nothing that they want. By hitching those goals onto a bill about something else that is more popular, there is (or was) a chance that they will be able to pass some aspect of what they want, rather than nothing of what they want. Hence, "child care" is now considered "infrastructure", even though nobody would have ever argued this before 2021.
Isn't it better to get something done than nothing?
That depends on what you value getting done. Some people want the government to get things done, generally. Other people want the government to do only specific things. Other people don't really care what the government actually accomplishes, but wants showy moments where they can perform on cable news and the internet according to what their voters what to see. All of those people are participating in the legislative process and therefore steer it towards this conclusion.
Or is the risk that once something passes, the GOP will say that they accomplished an infrastructure bill and not even come to the table for anything else?
The GOP is not going to come to the table for anything else anyway; they were not sent to Congress to pass progressive policy priorities. The only question was whether or not Democrats could get a few of them into voting to pass some policies they would otherwise not under the guise of "infrastructure."