That's an interesting question, Fay. My argument would be that a showreel is only a useful bonus when you are starting out - it can help you win representation because it can save agents the time of having to see you appear in something or conduct an interview with you in person - but, truth to tell, many of the best agents still refuse to take on a client on the basis of showreel material alone. They would still ideally like to see you perform and/or meet you on a personal basis before they agree to take you on, though a good showreel might get you noticed in the first instance. But I agree with what you are saying - if you are a theatre/MT etc. performer and this is really where your strengths and interests lie, then you will be ideally placed with an agent specialising in theatrical castings - and, at the risk of generalising, many of these agents remain quite 'old school' in their values - they are unlikely to place much stock on showreel materials because, as you say, their primary areas of casting interest are not screen based!
It *is* worth knowing that you are a stage actor by vocation (i.e. that all your interests and enthusiasms are rooted in stage performance, and that you have the sort of look and skills base that will guarantee you a lot of lucarative stage work - it's much easier to win if you are a 'triple threat' performer who can sing, dance *and* act - as well as possibly play musical instruments - in this day and age, for instance). Many actors start out as 'stage performers' because it is much less likely that amateur, school, university level work, youth performance, fringe material etc. that may generate the initial enthusiasm for acting will ground the actor in anything other than stage work. It is only later that many actors discover they have a talent for screen performance, or voice over, or commercial modelling or whatever the specialism may be. Still, to stick to the point about showreels...
It's worth noting that there is no point in : a) crafting a showreel together from mediocre material - particularly if you want it to open doors with casting directors - agents may be *slightly* less choosy about this, because they may not care so much if you are showing broadcast level work, so long as your acting is good - but a good showreel ideally features broadcastable material, which is admitedly a bit of a 'catch 22' because its hard to get cast in broadcast level material without an agent - though agents like to see you can work in this type of material because it promises returns on their investment in you! The trick remains to try and work as hard as possible, through CCP and other sites, to win work on as many decent sounding, if low budget, film projects as you can, source as much of the material together from them as you can, and then edit (or get someone else to edit) the showreel together carefully and impressively, so that it says to an agent/casting director that you can cope well with the demands of screen acting, and so are worth sending to auditions. I will point out that it took me about four years to get enough material together for a two minute showreel that I am happy with; some actors get more screen work together faster, but it really should be work that is solid in terms of performance and of production values, and this is not always easy to find.
b) There is no point in incorporating stage work into a showreel (unless, perhaps, its intended for an agent). Some actors will argue that a stage show that has been well shot can be effectively incorporated into a showreel - but it's not a question of the quality of the reproduction - its a question of what casting directors are hoping to see from the showreel, and, if they are casting for screen material which all who will demand showreels are, then they want to see proof of the ability to act for camera, not proof of the ability to stage perform. If you incorporate a mix of stage and screen work, obviously this lessens the criticism, but, trust me, many casting directors still think including stage work on a showreel makes you look like someone who doesn't understand the real demands of film and TV.
As a final point, it is natural that a lot of agents *do* prioritise casting for screen work, and so will no doubt welcome a showreel being made available - and this is for the simple reasons that screen work (of some description i.e. including commercials, in house videos, Internet virals, music videos as well as prime time BBC 1 series!) is generally more widely available, and is undoubtedly more lucrative than any stage work that might be generated. But you are quite right that there *are* agents who still specialise in theatre out there - it is just up to you to seek them out and apply to them!