To answer the question: **no downside**.
I prefer to charge up to 4.1v to make my cells **live longer** but that's unrelated.


The key point you make is:
*"so long as the maximum current is **limited** to a reasonable value for the cell (say 0.5C)"*
That alone will make it so the 4.2v you aim for will be dropped so as to push only 0.5C in the battery at a given instant.

**My experience:** I actually tried to push a **constant** 4.2v with **NO** current limit through a li ion cell.

The amps can reach **double digits** and the cell hates it so much that it heats up like crazy.

That would be an **excellent way to start a fire**, so yes, **DO** limit current to manufacturer recommended values.