Nice but it won't suppress weeds. Really, nothing you can walk on will. I use creeping thymes, but still have to weed (and periodically mulch bare spots.)

My paths are grass. I just mow them.

I use mulch and have for years. I don’t find I need to replace it every year. I often use sawdust from a nearby sawmill or chips from line trimming crews or the local arborist, so free.

IME moss doesn’t stand up well to foot traffic and doesn’t suppress weeds in situations where there is enough light to grow weeds.

Round Up (not environmentally friendly) kills weeds without harming moss. Stepping stones in the moss are best with foot traffic.

My sister made a moss rock garden https://familyfocusblog.com/make-moss-rock-garden/ but I think that moss would be too sensitive to use for a path that would get a lot of foot traffic.

I've found moss generally uncooperative. It goes where it wants, but not where it doesn't (which is, of course, where you want it to go.) Even transplanted moss doesn't work with surety.

Editing to reiterate Bab's point that mulch doesn't need annual replacement ... just top dressing.