I am not just talking about "the website". These reasons are given out via all forms of media - websites, yes, but also over the phone, help points, Twitter - and on CIS and train/station PAs. You'd think that the people (including guards and drivers) updating these various systems must have a very slight clue about what the issue is, even if they haven't got the train's technical documents to hand and don't have qualifications to work as skilled fitters/medics/signallers/whatever else. They will not be sitting there for a couple of hours with the only information being that a "problem is under investigation". All these methods need central control as they are crucial sources for all sorts of people. If it isn't a priority to provide information to customers who pay and enter into a contract for their transport, don't bother doing it!
Passengers definitely do care about what's delaying them - if you tell a passenger moaning about "another supposed train fault" that the brakes have jammed on and the train is stuck in a tunnel, I know from experience that they will generally say "Oh, that's quite a bad problem, I guess we'll just have to wait" - if, however, you say that the train is faulty, they'll think it's like when their car takes a few goes to start up on a cold morning and that the train company staff are just being a bit silly. Likewise, if you say that an injured person is being treated on the line, they can empathise a bit more, and often will. Hence why people moan about "another person being hit by a train" on Twitter, but then apologising once it is pointed out that the person is sadly deceased. The first question is very often "What am I going to tell the boss/my wife/my kids/my dentist/my interviewer?" - rather than "How long am I going to be?"