201 billion eligible recruits, for an organisation which operates in terms of a few million active personnel at the best of times. and could easily streamline the roles required to function in wartime, not to mention the usual surge in interest that we tend to see under such circumstances.
There's no need to draft is my point, just the opposite, regardless of the ethical questions.
Of course the OP's point is that stories revolving around those ethical questions would make for good trek, which I completely agree with, but it would be difficult to work them into the setting without it creating yet another "How big is SF?" "is there money in the 24th century?" style circular fan debate....
I know, I just don't see them either having to or being willing to ever make that decision. They wouldn't force people to serve even if they didn't have such a large pool to draw from.
In the novels, there was no draft during the Earth Romulan War. When they did have a lot less people to call on and faced the destruction of Earth. If it was unthinkable then, they won't do it in the 2370's.