The difference between EV and reflexive equilibria seems to be that in the former, lower level desires are changed to match higher order desires, whereas the latter involves changing both higher and lower order desires till they are consistent. As such, it involves much less changing of lower order desires, and much less overall changing of desires, as you have more degrees of freedom to work with.

There is still some risk - as you say, maybe there are few attractors - but overall RE seems a much more conservative approach.