Full Idea
It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions.
Gist of Idea
If we accept that V=L, it seems to settle all the open questions of set theory
Source
William D. Hart (The Evolution of Logic [2010], 10)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.270
A Reaction
Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist.