The first bold bit.... no it's not. It might be the main bit but a good goalie should help marshall the defence too and be a part of a collective defence that preempts and prevents chances. For example, the Southampton goal.... he didn't need to save the header (and didn't), he needed to come out and punch/gather the cross like 90% of goalies would have done and prevent them even having a chance. Moving off his line and positioning have always been major flaws in his game but in the past, his miraculous ability at shot stopping has gotten him (and other defenders tbf) out of jail. I'd rather prevention than cure.
The second bold bit.... as others have said, just no. He comes out a.couple of steps and Palace struggle to score that winner.... he sees the cross about to happen for Southampton, comes out and gathers/clears it, they don't get that equaliser. That's not to say the defence shouldn't have helped too but they were goalie errors and given his age, I can't see him coming off his line more in the future plus his ball playing ability (at feet) is average at best. He's getting left behind compared to what a modern goalie is asked to do and especially one where the team are told to pass it out (as we now seem to be).
Great goalie in the past, good one now but not one I'd give that contract too. Not for him and not for the precedent it helps set/perpetuate.