Does a trace with via handle more power?
Well if you have a very thick trace to carry a lot if current on one side and you want to flip to the other you often use a bunch of vias.  Vias have their own current carrying capacity per thermal rise just like traces do.  

So what often happens is an engineer has to do this so instead of calculating how many vias they need they just add more than they think they would possibly need just to be covered (since normal such vias are very cheap).  Each via in parallel is like a wire in parallel the current will be split (more or less) between them.  In some case such as very fast switching of high currents the location of the vias might matter, so the split might be a little different in that specialized case.

Here's a link to a pcb via calculator that includes current carrying that might be instructive.