The requirements for air-defence are now higher than earlier - likely both for sensors as for effectors. The unmanned ships could have lower standards - but if they should contribute to the sensor network, they still require good sensors. Certainly for each ship not to level of SPY-6 plus and X-band radar as on high-end ships - but combined it cannot be much worse if it should be be able survive e.g. against the Chinese Navy. I am not sure what kind of radar would be useful for such a network.

The US definition of a frigate as an escort is only one definition. The RN calls ASW ships designed to hunt submarines frigates. There are frigates designed as true multi-purpose ships, which can operate independently (which is not so different from acting independently with an escort of drones - these are only different generations of ships, not different types).

A FREMM could certainly be used a mother ship for drones - it is spacious enough. The smaller Mogami was designed for it. The reason for the Mogami being cheaper is likely the well working, modern Japanese ship building industry (which continuously builds new designs, not old 1980 design ships and which builds also a lot of civilian ships) plus an order for 12 ships.

The aim to build a cheap ship is fine - I do not argue against that. E.g. Singapore's 8000 t Victory class is claimed to cost only $200 million (but I assume without armament). That is a design optimised as drone carriers and they will have an air defence superior to a LCS.