peak normalizing is a pretty standard practice, but RMS is not. generally, when RMS normalization is done, the idea is to raise the average loudness to a specific level (ex: -6dB). This will most likely cause the peaks to clip, so usually the software will compress the signal, or allow it to clip. In either case, the results are undesirable. Over compressing audio is an easy mistake to make and although the source sounds more even in the end, you lose the dynamics of the music.
More often than not, people will use a little bit of compression to lower the peaks before they apply a peak normalization, it's a way to give yourself more "headroom" and is an acceptable practice - particularly if you're recording rock music.
I'm going to try to attach a screenshot of the project I'm working on now. You'll see what I mean about the peak values and the dynamics of the music. Hopefully your project looks similar.