That isn't how it works.  Within HEVC there are computational sub-profiles, just as there are within h264, so it's HEVC, Subtype X.  It's not a 2-pass process or a second data reduction procedure as your "double" implies.  Instead, 10-bit is a type of HEVC, as is 8-bit.

From what I've seen, HEVC generally needs to be 10-bit to avoid banding problems that can be worse than what sometimes happens with h264 high profile (8-bit) when the encodes are small.

btw, HEVC uses Main and Main10, not High and High10 profiles.  (You mentioned "h10" but it would be "m10".)