Fan coil units work just fine, you’ll need to install a condensate drain but other than that it works like a mini-split evaporator/fan air handler.

You just have the added equipment and maintenance for the water/glycol loop vs an air to air system that only pipes refrigerant around. Fan coil units or VAV boxes are the usual terminal units for commercial HVAC systems that have a chilled and hot water loop, VAVs are used in a system with ducted AHUs and FCUs are used for apartments (stacked FCUs with vertical supply/return risers) or spaces not served by ducted air handlers for whatever reason.