I have a slightly different answer and experience to
@Tone-y as I certainly remember seeing PRS guitars in the late 80's early 90's. I must admit though that they were 'rare' - like Parker Guitars but they certainly had an audience and could be seen in most of the shops in my area unlike Parker which were very rare to see. They weren't 'common', it wasn't as if every 'bar' playing band had anything like a PRS and at most, you would see a proper Gibson Les Paul which was probably bought second hand before the whole Vintage thing blew up. Only famous bands had a Les Paul custom shop. It was seeing PRS in a guitar shop that made me want one, made it the ultimate guitar - the Waynes World it will be mine, oh yes it will be mine Guitar. It replaced my Gibson Les Paul Custom in Wine Red as my 'dream' guitar as soon as I saw one - I never saw a Wine Red Les Paul either - other than in a shop...
You could equally argue that the Ibanez Jem never came to prominence in the UK as these too were never really seen other than in a guitar shop. I think a lot of that though comes down to price. Your average band weren't really playing PRS on stage - much like they weren't playing any high end guitar on stage. I honestly can't say I remember seeing them anywhere other than a guitar shop or in Guitarist magazines. At most you would see a video of one of the American bands of the late 90's playing PRS but the shops around me were selling PRS guitars - not in huge quantity but enough to see new guitars in and older stock disappear. For example 'World Guitars' a high end guitar shop that Rob Chapman (of Andertons and Chapman guitars) started doing video demonstrations for is literally just down the road from me - within 20mins drive. Someone must have been buying these guitars.
Prominence though is perhaps too strong a word. They certainly aren't or weren't common to see if you exclude the shops and the obvious turn over of stock. My 'Waynes World' dream guitar would have to be replaced as the guitars would disappear from the shop, sold to someone, and be replaced by another similar PRS. The very late 90's and 2000's were not as music focussed for me as I got married and had kids so any thoughts of pursuing music and obtaining a 'dream guitar' disappeared so I stopped looking.
High end guitars have never been 'common' to see amongst the bands I used to see in pubs/clubs etc. Santana was still the most famous player of PRS guitars. I can't recall anyone I saw live actually playing a PRS and only tended to see them in guitar shops but they would disappear and be replaced by 'new' PRS stock. I only know this because they were my 'dream' guitar and would be replaced by a different dream guitar as they sold. These were like Ferrari's or Lamborghini's of guitars - the very high end instrument that people were obviously buying but once they left a showroom, you rarely if ever saw them out in the 'wild' so to speak. They may well of been bought as a 'trophy', a studio/home use 'prize' guitar that people didn't take to gigs as those who bought supercars didn't drive their prize motor to work every day. I really don't know - all I know is that PRS guitars, as well as adverts in UK based Guitar magazines had PRS - generally the most expensive guitars in the shop - and these would sell periodically so some people must have bought them.
There are UK based guitarists here who own PRS. Maybe they have a different perspective but I kind of think that unless you were a Professional recording musician, High end instruments just weren't used for gigging. There seemed to be quite a gap between bands that had made it and the rest who were 'trying' to make it - the bands doing all the pubs, clubs etc. Those that hadn't were generally playing guitars under £1k and those that had were bands that tended to be 'Gibson' or 'Fender' - maybe Jackson or Ibanez.
As I said, my experience is likely to be different from some as I missed the whole era of the SE release and subsequent decade due to family commitments so I am only referring to the first 14yrs of PRS (from their first factory onwards) and haven't really been actively going out to pubs/clubs etc since I separated and divorced which has enabled me to return to trying to play guitar. I am only speaking of the pre-2000's when I say that bands weren't using 'high' end instruments - inc Gibson - unless they were old and obviously used before the vintage market made these 'something' special. The 'few' opportunities I had to look in a music shop to look at 'dream' guitars, look at something that were drifting further and further away - even more of an unobtainable dream, I would never see the same instruments twice meaning that their stock had at least been replaced.