Tighter analysis of modified Borůvka's algorithm
It is possible to craft test cases for general graphs where your Borůvka's step wouldn't
halve the number of edges in each step, even though it halves the number of vertices.
An interesting note is that the optimization that you suggest works for planar graphs. This is because
for planar graphs $|E| \leq 3*|V|-6 $ i,e $|E| = O(|V|)$. And in general it leads to a
speed up for the class of minor closed families of graphs.

Reference:


Masters thesis, Claude Anderson (on page 100 the worst case input for Borůvka's algorithm 
is described). [link]
"Two linear time algorithms for MST on minor closed graph classes". Archivum mathematicum 40 (3): 315–320, 2004. [link]