I agree with you on this one, the way starships move around does suggest the impulse drive is indeed a coil drive specialised to work at slower then light speeds, also it would explain the tremendoes acceleration and the little fuel it uses.
We don't know how much fuel impulse engines require under normal circumstances, but if the NCC-1701 employs degenerate matter as reaction mass - say something like metallic hydrogen
- it would to a certain extent explain, A). the Enterprise's on-screen performance for velocities < c
, B). the apparent lack of fuel tanks that would otherwise take up ~99% of the vessel's interior volume, and C). the discrepancy between TMoST
's 190,000 ton mass figure and Scotty's "almost a million gross tons of vessel" line in Mudd's Women