I WFH though travel to client site for work most weeks (currently 2 days a week, was 3 days a week last year). This is in software consultancy & implementations. My job normally involves working on 1-2 year projects on client site, so employer expects me to be out of the office most the time anyway. So WFH was a logical extension of that, already have the remote connectivity set up, had been working for company for about 7 years and colleagues used to email/phone contact. It came about because I asked politely with good notice and had FU money had they said no.
I think there are plenty of jobs where part/most WFH is perfectly feasible. Lots in IT, research, consultancy. Though with consultancy/freelance/contracting get into a "work on client" site maybe more than WFH. And 100% WFH where working with colleagues had only met once or twice might be a bit problematic during times of stress. But then again, if you work for a large company you may regularly work with colleagues in other offices/countries who you've never met, even if there's no WFH.
In terms of which jobs really allow WFH, there are a few modern companies that do it explicitly; some more enlightened ones do it semi-formally (one I've heard about prefers people to WFH part time as they don't currently have the office space for everyone to have a desk and don't want the cost of having it); some may offer it informally and there will be some where the owner is a "want to SEE people working" person so won't allow it. Avoid the last set. Pprobably you're in a better position to ask after establishing a good record for a year or two (proving you get the work done and solve problems), and using the occasional "need to stay at home today for electrician to come round" to prove you're still responsive on those days. Secondly it probably really depends on your manager, some may feel against it for undefined reasons. Asking for a 1 day a week trial as a starting point could work (my WFH was agreed on an "as fits business needs" basis), then increasing it over time.