I've recently started commuting on a road bike (I commuted on a mountain bike previously and still do on wet days). I had to change my route to avoid gravel while on the road bike. This link is a Google Maps street view picture from my new route:

Link

This is a commuter artery with side lanes for residents to park. Cyclists are encouraged to use the side lanes (there's even a cyclist in the street view picture!). However, it only took a few days riding in that lane for me to switch to riding on the main road because:
1. In the 11-block stretch that I travel, there are 6 streets intersecting the main road (every two blocks), and most have Stop signs. On the main road, there are only 4 lights, usually green.
2. In the side lane, note the blind corners (fence, shrubs) on the right side. No carelessly blowing these stop signs, so you lose a lot of momentum along there.
3. While in the side lane at the stop sign, one must watch for cars whipping into the lane from the main road, both from behind and ahead. You need to be damn sure that no one is going to be turning in before proceeding past the stop sign.

On the main road, yes I have to be vigilant, but I still feel safer being on the road. Plus, I don't lose momentum, so I get where I'm going faster.

This road, however, leads to a MUT that I do take, and I have several kms of unimpeded travel until my next turnoff. It's very quiet in the mornings, a bit busier in the afternoons, but nothing unmanageable. So, whether I take the road or a MUT is really situationally dependent. But I wanted to point out a situation where, in my opinion, the road is a much better option than the parallel MUT.