Replace 3.5 mm AUX with USB
Assuming this is a line-level signal, sure, you could replace the 3.5mm jack with a USB connector.  But why?

It would likely be a lot simpler to simply repair or replace the existing jack.  It my simply be a bad solder joint to the board.  If the jack itself is bad, you can probably find an exact replacement with a bit of looking.  Even if you can't find one that fits the existing footprint, it's still probably going to be easier to fit a new 3.5mm jack even if you have to do a bit of bodging than to try to fit a USB connector there.

The 3.5mm TRS connector has some drawbacks, but it's been the standard for this sort of thing for a long time with little trouble.  A bad experience with one device doesn't really warrant such an extreme response.

If you do have repeated problems with cables failing, you might want to look for a cable with a right-angle connector at the speaker end.  This may reduce the strain on the connection and improve the lifespan of both the cable and the speaker connection.