Are there any aircraft where minimum-V1 is limited by Vmcg?
Yes

Almost any transport category jet will reach its Vmcg V1 limit in favorable conditions.

The rationale is quite easy: When fully loaded with heavy fuel load (ie. at maximum takeoff weight) some 20% of weight is payload and about 20% is fuel. When the same jet is taking off with light passenger load for a short hop with low fuel load, there is massive surplus of thrust available so there is some acceleration available in case of engine failure on ground. This is especially true for twins.