I have heard that expression, a dying trade, but to me that makes it more worthwhile. If less and less therapists are bothering to train in it, then it's harder for clients to find a therapist, so they will seek you out.
Many clients need electrolysis... for varying reasons. Some may have an obvious beard, which in my opinion needs to go(!), some may have just a few course hairs that need attention every now and then, some like to have bikini and underarms done. For breast hairs, I think electrolysis is pretty much the only option. I'm not trained in laser, but I'm under the impression it's more suited to denser hair growth, but when hairs are sparse, it's pretty easy to pick them out with electrolysis.
It's a treatment that's very easy to cross sell. When clients are having other treatments you can tell them about it and often they will go home and mull it over, then decide to give it a go. There are also clients who don't have anything else done except hair removal because it's the only thing about their appearance that really bothers them.
With hindsight, I'm pleased I trained and made the investment in the equipment etc. My diary is definitely more full by offering electrolysis. You have to have a bit of patience and it can be a little bit fiddly, but it's also very rewarding.