a type of web-of-trust), that provides a lower grade of security, but at a much lower cost (so we can afford a very large quantity), is good for the 2nd line of defence, that we use against 51% attacks
However I do not agree that the proof-of-work is made irrelevant by the proof-of-stake idea. Rather I think that they provide solutions to different problems.
The fundamental problem here is that these things are not generally additive: An action which causes different nodes to follow different chains is a forking attack which may be fatal to Bitcoin.
Say you have two distinct perfect security measures: A and B. They both do a nearly perfect job of selecting the best chain. But they are distinct and can select different chains. Some users use A and some use B (or some A, some B some A&B) then an attacker just has to do something to make them differ that something may even hardly be an attack and then Bitcoin is forked in a way which is irreparably without manual intervention. Rapidly people will double spend on each of the forks and within a dozen blocks or two any repair will be a difficult selection of which of two enormous groups of people gets robbed more.
Even the cases where the node just shuts down in response to reorgs which is much better than the above still is no help. In a sane attack the reorg you see is the reorg moving you back onto the real chain by the time you get any evidence that something is wrong it's too late. You can't ignore that reorg without forever losing the ability to trade with everyone else. The shutdown just helps you avoid getting exploited again shortly thereafter. But even that isn't much help because at the same time you've exposed yourself to a nice DOS that you were immune to before. If miners adopt software that shuts down on reorgs then all sorts of great force multiplying attacks happen where you get >50% active hash power when you really have much less, just by first getting luck enough to trigger a big enough reorg to knock miners offline.