It should be possible to change ones mind about something.

Lots of conscientious objectors do so from a religious viewpoint, but having a conscience is not exclusively reserved for people of some religion, you are welcome to have one all by your lonesome. And that conscience can start to ask annoying questions about your actions and affiliations which can cause you to change your mind about something.

What is more worrisome to me is that it would be something that could be refused. If someone states they have no will to obey the government entity they have applied for then they should be allowed to leave. The alternative feels too much like ownership to me.

Oh, I agree with you completely. That doesn't necessarily mean it works that way, though. Conscientious objector status requires proof, and as I understand it the burden of proof is on the objector. I could easily imagine that that burden of proof would be higher if the objection occurred after initial acceptance, especially voluntary acceptance.

My father was eventually granted CO status after spending a year in the stockade for failure (well, refusal) to report for active duty. I don't know how things there have changed since Vietnam though.

I imagine it's quite a bit more difficult to argue int he absence of a draft.