Why can I not skip many of the cut scenes?

There is, you just missed it. Go to your controller settings and check what key (if you're using a keyboard) that's assigned to skip the cut scenes.

skip 

esc 

You still can't skip much of the beginning of the game's cut scenes and even when you skip the cut scenes at the beginning of the races you still have to watch some of it.

Actually I've been forced to watch the intro with the tutorial every time I entered the game no matter how many cars I've changed in the previous attempts and, no, there's no way to skip it.

I know this is old post, but may be helpful to others.

I just renamed one of the files in the installation folder (Program Files (x86)\Origin Games\Need for Speed(TM) Most Wanted\UI\MOVIES). In my case the file was named "1307304.VP6". I renamed that to "1307304.VP6.skip". It was the largest file in that folder. You can also load the files with VLC media player, although without audio. That seemed to work.

These forced intros/cut scenes do my head in when there is no way to skip, plus they seem to take forever to load.

Its probably because the cut scenes are a way of hiding loading screens. There never that long it's just the quality of the voice acting its always always SUPER CRINGE AND BADLY DELIVERED!!! I think they hire cheap voice actor's due to the cut scenes being almost a throwaway thing. Just there to set up a race of the fact the FEDS are chasing you.