Checkpoints within a fight might not work mid battle per se. but checkpoints as a whole could be great and its something that's been suggested multiple times.
All it really needs is like 3 simple checks and lock out various queue options if the answer to any is no.
A: Have you entered the fight before?
B: Have you made it to the phase 3?
C: Have you got the boss down to lower than 10%?
If the answer is to A is no then the only option you or the party leader have is a practice party for the first phase within raid finder.
If the answer to A is yes but B is no then you can queue phase 1 learning parties.
If the answer to B is yes but C is no then you can queue a phase 1 or 3 learning party.
And can only queue a "clear party" if you or all members have seen lower than 10% boss HP.
This could be a really helpful tool as it would prevent people from joining the wrong parties. in a similar fashion to the duty completion check box they added to party finder groups not so long ago. If you created a clear party with that check box ticked then anyone who had not seen 10% HP on the boss could not join your party.
would also help raid finder groups as well. nothing worse than queieng a fight in raid finder only to find a bunch of people who have never entered before have selected the duty completion option instead of practice...
if it falls to the party leader to kick people out for performing badly or joining the wrong party the problem there is that it's generally to late and everyone elses time has already been wastred.... a check point style thing would prevent this before it happens in the same way the duty completion requirement does.
it wouldn't be perfect obviously the same way the duty completion one isn't 8 people who have completed a duty can form a farm party and it can still fail miserably. but it does at least increase the likelihood of a group being successful