Use of ICE sets on routes with no HSR

Hi all, hoping someone here can satisfy my curiosity - why does DB operate routes with ICE trains that could be served by non-HSR equipment?

Currently on ICE1229 which goes from Cologne to Vienna, but avoids the cologne to frankfurt HSR, and then (I think, comparing the route map and a map of the HSR infrastructure!) is on conventional tracks all the way to Vienna.

This is being operated by an ICE3, which seems like overkill for that route. Is there a reason DB uses expensive HSR capable trains on routes that don’t require them?