I believe the reason we see these effects is partly down to the setup most people tend to use for Spain(which can be applied to most other tracks).
As we all probably know, you need hard ARBs, hard springs and high camber to be able to maximize your setup around that track for qualli, otherwise you find yourself understeering on certain corners, especially T3(up the hill to the right, you burn out your left front around here), T7(more huge forces through your left side tyres) and the final chicane(which you need to have an ultra-responsive car to be able to slide it through that complex).
So what happens IMO is that the AI has a preset "setup" in terms of tyre wear, downforce etc. If I remember right these are just numbers in the registry that are adjusted track to track to change the AI performance to suit the track, and to get accurate wear compared to the user.
But then when the user alters their setup to have extremes such as the springs/ARB i mentioned, or simply just using too little/too much downforce then what is optimal, your going to have slight performance differences, and most notably your going to be trading 1-lap performance for tyre wear, so that is why Rosberg and the rest of the field will drop away in the early laps, but then when he switches to primes and your on options and burning them out at an extra quick rate, hes going to have a tyre life advantage on you at that point.
If you need to adjust the AI track to track just go DL that registry editor from 2012, go into the settings for the AI pace for individuals tracks, and make slight adjustments as necessary for you to have a competitive racing experience with the AI. That's what I do, as I play through my seasons I'll just constantly adjust the AI performance/tyre wear etc.