Horrible idea.
For 10 man there is no reason to do anything beyond the latest boss. The others don't drop anything better than could be obtained by farming heroics as their gear is iLevel 232 or lower and drops triumph badges. If you need any of this gear you can go farm heroics and get it yourself. You are also being carried by the raid as you aren't the appropriate gear level for the final boss.
For 25 man I expect to do the 2 most recent bosses as the 245 pieces are better than can be obtained from heroics or triumph badges and may still be needed by a number of people. The other 2 are below the level of gear you could get from badges from heroics and once again if you need that gear you are being carried by the raid.
Any idea that requires you to kill them in order is even worse. You can end up getting saved to an instance that isn't able to kill all the bosses and then good luck trying to get a new group formed back up with an already saved instance.
With 4 different tiers of difficulty and gear the only ones that are relevant at the most recent one or two at most. Anything that tries to forcibly change that is just going to be a horrible idea full of problems.
With that all said I don't typically drop the instance if the majority want to keep going and clear the other bosses but I don't feel at all bad if it falls apart and we don't kill the other bosses.