In my experience, going from a hardtail mtb to a road bike did speed up my riding, but not that much either, it's not like I'm cruising at 20mph but that's probably my fault, not the bike's.

A road bike, even one with a relaxed geometry, will give you a more 'aero' position than the hybrid. It would also come with higher gears (bigger chaing rings) so you could pick up more speed (I'm assuming your hybrid has MTB gearing).

If you currently have a 44/32/22 or similar MTB crankset and you commute is mostly flat maybe changing to a trekking crankset (48/38/28) could be a convenient way to pick up more speed without having to change much of your setup.