I've found it's a great way to get into hiking if you don't have all the gear to start off with, or if you're encouraging others who might initially hesitate at staying in a tent (think candles + a wood fire and room to sprawl on a stormy night). Roof water is a nice convenience too.
Of course using your own shelter ultimately gives you much more range & more independence though. Sometimes your tent will be cleaner/better smelling/less rat infested than a hut. And as someone mentioned relying on getting to a hut for shelter can catch you out if you get lost or misjudge distance: you still need a backup which some don't realise.
Only a very few have solar powered lighting + gas stoves. Some of the large huts on the popular South Island walks (eg Routeburn) are more like hostels than huts (40+ beds, booked out every night during peak season), which might not be the experience some would be after. But it does make it accessible to just about anyone, and to be fair the campsites are busy on these walks too.
Some on the other hand are tiny things with lots of soul that have been around forever, in some awesome remote spots, & during winter unvisited for weeks at a stretch. Much more part of the experience.