There are currently three strategies in different navies:
a) adding MCM equipment to frigates (high-end warships, US and Japanese navy)
b) adding MCM equipment to OPV (low-end naval ships, see Australian navy, see also the Canadian Kingston class)
c) building specialized MCM ships (e.g. Belgian, Dutch, and Finnish navies, probably also the French)
For sure, a) and b) are cheaper than c) if considering the costs of the complete fleet. In case of war, a) can defend itself better than b) or c) and protect its drones used to hunt mines.
I do not think that the drones are the new aspect. They exist for some time - for sure, they are getting better. The new aspect is the building of multi-purpose ships, which include also MCM as one of their functions. E.g. the use of specialized mine-hunting sonar in a multi-purpose frigate.