Crossfades have been SOP since we were making edits with razor blades. Back then, you always cut tape at an angle so that you wouldn't hear the splice. Digital audio is no different, just much easier.

Whenever you split a clip, put a short fade at the split point. In most cases the fade can be very short, often less than a millisecond. Sometimes you'll need longer fades, especially if there's a lot of noise in the track (e.g. a vocal recorded live with the band playing).

I do audio edits a lot. I set the snap to grid to whatever resolution I want..... I split the clip in 2 places... before and after the event to be replaced..... I highlight that clip and set my punch in out points automatically and then set the now marker before the split and hit record. 

The punch in is totally silent... meaning that there are no edit clicks in or out.  

Those clicks you hear come from a non-zero crossing edit split.....or from a non perfect drag and drop.  There is an option to have all splits occur on zero crossing points and I believe it is set that way by default. 

Using a third party editor or trying to make non snap to grid edits are very often problematic. It is virtually impossible to get the 2 clips to line up properly so that the click is not audible. 

Try the method I suggest in the first paragraph. For me, that is a flawless way to fix an error in an audio track.