Wifi N 4x4 router with multiple 1x1 clients - any benefits?

Since wifi N doesn't support MU-MIMO, is there any benefit of having a 4x4 router when all it's clients are 1x1 devices? Won't 3 router antennas just sit idle all the time?

Not quite. Modern wifi (ac/ ax) supports beamforming and MIMO also profits from that - not for a single device, but for multiple concurrent simple devices. 802.11n is a bit far into the past, beamforming didn't exist then and MIMO was in its infancy (more like antenna diversity), that doesn't mean the antennas would be useless, but you won't profit as much as with more modern standards.

It does, however, support SU-MIMO (Single-User MIMO, or just "MIMO") serving multiple spatial streams to one single client at a time, in contrast to MU-MIMO being able to serve multiple clients concurrently.