Personally I use normalizing a lot. If you have a lot of clips it may save a lot of time.
If you mix modern music (with compressors and other hard hitting plugins) with audio material recorded well at 24 bits, normalizing makes no difference in the end product. If you use the track/clip gain or plug-in trim instead, you'll end up exactly in the same place. Normalizing is basically just a gain change and nobody can mix music without changing gains anyways.
There are only two exceptions when it
may make a difference. In both case you need to use 16-bit audio and destructive editing to make a noticeable difference.
#1. If you normalize the track
very low, and raise the gain after that, you will lose information.
Like this:
original audio (16 bits) 123456789ABCDEF
normalized audio (16 bits) 6789ABCDEF-----
regained audio (16 bits) -----6789ABCDEF
#2. If you go crazy and keep normalizing the same clip up and down and all over the place.
If you use 32-bit-deep files, there is absolutely no risk in normalizing. None. Just don't normalize the clips to 0 dBFS when mixing. Go for -3 dBFS or, even better, less (I usually use -12 dB to keep a healthy headroom for mixing).