The question is more how long the system will keep functiuning if everyone click this button. It cannot work for too long if everyone is 100% selfish motivated with no other motivation than making selfish profit. It just fall down after a while like a ponzi schemes.
I only wanted to point out that the illusion that 51% of the nodes are "honest" and "willing guardians of the protocol" (of course including the emission model and the 21 million coins) is, well, totally deluded, and if you give the people the *technical means* to cheat, of course they will ! So the REAL reason that they *behaved* honestly was not that they had an intimate desire to be honest, but that they were *not capable to cheat profitably*.
Illustrating the thesis that what keeps "honesty in place" is the impossibility or the lack of advantage to cheat, not the "will to be honest". Honest behaviour is hence an emergent property from the rules of the system that makes that individually one wouldn't know how to be dishonest in an efficient way, not because "people are honest".
I think this is the case at large, in society, too, with honesty and "moral behaviour". It is the fact of not knowing how to be dishonest and immoral in a profitable way for most, that keeps them honest and morally correct. Not because of some intimate desire, but by the intelligent realisation that dishonest or immoral behaviour is most of the time, not profitable in the web of relationships. Government being about the only place (with its monopoly) where you have not these properties, and hence the place to be if you want to be immoral and dishonest.
BTW, the system would keep on working perfectly, because this is just like "bitcoin with somewhat larger block reward and tail emission". If one single click in the mem pool is accepted randomly in every block (you'd need a protection so that miners don't systematically take THEIR click), then you just get higher block rewards, that's all. But of course, the monetary belief in bitcoin would crumble, because the ILLUSION that it was a fair distribution to "honest people" (Miners) and now an *arbitrary* distribution to "cheaters" would break down. While as a system, nothing really changed.