I didn't know you could get them removed?
You certainly can, but it isn't an operation without risk. For me it was a last resort, but Dolly was so unhappy, sore and uncomfortable I felt it was a risk worth taking.
It requires a vet experienced and skilled at the op or you risk an incontinent dog amongst other things. Some vets will recommend a specialist do it. Dolly's vet does loads (he's considered a bit of an expert locally on the procedure) and has never had a problem with post-op incontinence. I believe the actual figure he quoted me at the time was a national 1 in 200 chance of incontinence.
It isn't a pleasant op either, although Dolly amazed me by coming home the afternoon of her op, still wobbly, stitches in bum, and going straight into the garden for a poo, like nothing had happened. (there isn't a "wincing" smiley, but I'd be using it here.) No incontinence whatsoever.
I do know people who've had their dogs flushed, and have found the problem disappears, never to recur. So I would still try the flushing before an op- it's certainly the least invasive way and it could give a great long term result.