Cross feeding was actually proposed by both Russia and Boeing, so some pretty smart folks think it's worthwhile
back then Shuttle was proposed as most cost-efficient way, but ended up as unreliable & crazy expensive. many things were believed as breakthrough, but only a few is living breakthrough. + as i said, scheme to not burn core stage until needful altitude is quite simple alternative. actually, it's just modification of multi-stage design.
Methane is useful because it has a higher specific impulse than keresene but doesn't have the handling, containment degradation and boil-off difficulties of hydrogen - especially long term. It can also be made on Mars from its CO2 atmosphere and hydrogen derived from local water ice via the Sabatier process. This cuts launched mass as you cam refuel locally.
Mars? c'mon! Musk's rockets barely get in ordinary orbits. if to say about long-lasting missions, Methane is useless too: it's gas, so boil-off problems shall be as well, leakages are yet another trouble which will not vanish into nowhere too. how weighty hardware you need to mine Methane in the Mars??? what about radiation shielding??? what about portable nuke reactors??? And so many others WTFs as well. & yes, what about oxidizer?
BTW, Russia's working on their new RD-162/RD-0164 methane fueled engines, so if it is an insane idea then it's a shared madness. One of these new Russian methane engines is in the same 650,000 klbf class as SpaceX's Raptor.
Methane could have some advantages, but for expendable rockets. however, even for expendable ones, it's very unlikely to get significant advance. liquid fuels have better ratio volume to Isp. in short, perhaps Methane will be fruitful for upper stages… but so far it's only theoretical assumption.