About to rope or not to rope the old school says: if you can catch yourself - there is no need, if not - to rope. Using protection is up to individual skills, similar to the rock - somebody can runout 5.6, somebody 5.12. The main part is you should be confident in your partner as in yourself, otherwise use protection.
As far catching people on steep slopes - plenty of history. Best example from my experience - we were travercing horizontal ridge, ice about 15 feet wide and one in our party broke crampon, next thing he was going down on 50deg ice slope, after full rope length (40m), my partner caught him with axe pick (not even shaft). although using some extra help as the third person jumped on top of him. The point is if you use correct self arresting technique, you need only a small extra pull from rope to stop. Back in Russia in 80's we had to pass tests to climb mountains, one of it was to selfarrest on 35-40 deg pure ice. If you can do that, you can selfarrest on any snow slope.
Oleg.