In no way do I mean this to come off sarcastically. How does a phelonic break tip damage the cue ball if it is made of the same material? The cue ball and playing balls are made of the same material as well, and hit each other constantly, but that doesn't damage them.My experience with the low-end McDermott cues has been good. A local billiard supply store lets you shoot with the cues on sale and the $100 (about) McDermotts hit the ball better than the $400 cues. Check out https://www.mcdermottcue.com/pool_cues_100-149.php
As for a break cue, here is some contrarian advice: don't get one. Many of them have phenolic tips -- the same material the balls are made of. Those tips damage the cue ball. This is easy to test and see, if you have a nice, new polished ball that you don't mind ruining. Beyond that, until your power gets up to the point that you are destroying tips, there's not much point. You are better off learning to control the cue ball on the break shot while learning how to play power shots with your normal cue.