The answer is a definite... "it depends".  
 
 

The "mostly yes" is an interesting answer. 
 
I think if I had a high spec'd laptop and used it every day for say a year with no problems, in exactly the same way as I do now with zero issues I might start to like it. I don't see that happening though. I have too much fun when it come upgrade time for the desktop. 
 
More to the point which I was drifting from. If we are going to get specific here, then specifically commercial studios or studios doing intensive mix work DO NOT use laptops on a regular basis as their mainstay computers. Anyone hoping to either enter that business or duplicate it won't use a lappy either. There are good reasons for that. I hope this doesn't come off as condescending. This is just a simple fact. It doesn't mean laptops aren't ok for the home studio. 
 
Since we are being specific and to the point, in that case laptops don't make good replacements for desktops. This is one reason why I think so many who have come from that background will use a desktop whenever possible. 
 
It isn't as difficult as seems implied to make the kinds of hardware changes necessary to a desktop to keep it updated. It's actually a less expensive way to run a studio if one chooses that route.
 
 

I think one of the other major attractions for laptops, besides the portable studio aspect, would be using it as a live performance gig machine, rather than as a recording studio.
 
If you watch the promo videos for various DJ/beatmaking software, they usually show a laptop as the centerpiece of the producers kit.  That may lead to many assuming that's all that it takes...
 
Which may be true, but still it depends on your needs.
 
I am aware that some Sonar users have laptops for live situations, but would bet most of them also have a desktop as well.

FWIW, I was recently looking at a laptop to take out (running Ableton Live) for live triggering of samples.
Wanted to be able to trigger those samples at ASIO buffer size smaller than 64-samples (for super tight timing).
 
No laptop would deliver the level of performance I was after.
Built a large Cube using a 6850k.  Performance power to burn... and no limitations.
Only downside is size/cartage

I can do that at 48 samples with my Fireface UCX. But I don't usually need to run in sync with other hardware or something and for live playing of softsynths 128 samples is just fine.

No, big budget commercial studios don't use laptops but
1. They don't need to be mobile because people come to them and
2. The discussion here seems to focus a lot on the role of "engineer" (whether it's in a big budget studio or doing mobile recording, bringing the recordings back to a big studio)

There is more in the world than home studio or big budget commercial studio. I'm a professional. I produce a lot. On many locations. And unless it's a live gig or rehearsal I'm recording, it's always been the case that I do some editing (a quick Melodyne?) or mixing (can we get an mp3 of what we did today etc) so it is really useful to have powerful laptop rather than something that just records. And when your laptop is powerful enough, there is simply no need to have a powerful desktop too. Yes, desktops "max out" at way higher specs. But I didn't even need to go for the overclockable K version of my i7 6700 - I simply don't max it out. I don't do extreme productions like orchestral movie scores but as a keyboard player I use lots of softsynths and I don't like to freeze any of them generally. I have a ton of 3rd party plugins that I use liberally. I believe my needs are probably above average, if not at the top of the spectrum. For that kind of use, a good laptop can absolutely function well as primary DAW, and doing so comes with perks as well as drawbacks.