Sure they could. Currently the system allows you to enjoy the raid with friends, but if you leave, you retain the checkpoint you got from your buddy. All they have to do is remove the second part of that. It should be saved only for the host of the game, and/or anyone that started the raid together from the beginning. Lets say you had done the beginning by yourself and you joined your buddy at the bridge, then sure you should keep the save. You earned your way there. But you shouldn't be able to just jump into crota without doing anything else and then leave while retaining the checkpoint.

It would make things hard and nobody would get the raid done. Think about it. What if the host could no longer play the rest of that week? It would make it hard to complete the raid for those that have little time. I personally am not a cp seeker, I do the raid 3 times start to finish. My group and I do it all in one sitting. So it wouldn't effect me, but for many others it would be difficult