One of the most annoying things about running a 1725 rpm motor at higher speeds can be the fan noise. Since the slower motor has a fan designed for its nameplate rpm, it can get noisy and loud when running significantly overspeed. The fan might even throw a fin if it is one of those cheap stamped aluminum fin types.
On a drill press, you likely will not get to the point of an overheating problem since the operation is intermittent. The bearings in the lower rpm motors may be the sealed type, and these seals can generate a fair bit of heat. Now, the manufacturer may not care so long as the motor makes it through warranty. But, chances are that a inverter rated motor may have shielded bearings, or grease labyrinth provision to keep the grease in the bearing without a seal rubbing on anything.
That being said, the allowable temperature rise of the motor is usually quite a bit hotter than you might typically find it running at anyway. Overheating bearings in an electric motor are largely a matter of proper assembly and machining of the endbells. Our local motor rewinder always runs in a big motor after an overhaul and carefully checks the endbells for rate of heat rise.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)