Your intuition was spot on! I used to cut concrete for a living, and we had several hydraulic chainsaws. The torque on those things was incredible. They were quieter than gas chainsaws, even factoring in the diesel-powered hydraulic pump in the trailer nearby.
The main drawback, as other commenters mentioned, was portability. The saw itself was shockingly light (which made the torque that much more surprising) and portable - until you ran out of hydraulic line! Plus you always had to watch your lines to make sure they weren't going to get cut by a blade, pinched under a falling piece of concrete, or crushed under some piece of mechanized equipment.
Interestingly, there were three lines - hydraulic in, hydraulic out, and a water hose to spray on the cutting surface and keep the dust down. It's been a decade since I worked that job, but I still clearly remember the feeling of revving one of those things up, watching the water fly everywhere, and grinning as I just carved straight into a solid concrete wall - rebar and everything. It was a delight.