The whole point of a mesh system is for the APs to self-assemble their own wireless backhaul connections between APs. If you have wired Ethernet drops that you can use as the backhaul for your APs, you do not need a mesh system per se.
On the other hand, even if you don't need the mesh feature itself, mesh products often happen to make it easy to administer your whole multi-AP system in a coordinated way. But there are also non-mesh systems that also do a good job of making it easy to manage all your APs in a coordinated way. So it's kind of up to you if you know of a mesh system that has features you like, you might choose to use it for those other features even if you're not using it for its mesh features.
People in your situation often buy a wired-only home gateway router to go in their wiring center next to their patch panel. So your broadband Internet link comes into your house, goes to your modem (hopefully it's purely just a modem; it just directly forwards packets between the broadband port and the Ethernet port; no NAT, no DHCP server, no Wi-Fi AP), and then from the modem to the WAN Ethernet port of the router, and then from a LAN Ethernet port of the router to a gigabit Ethernet switch with enough ports to light up all your Ethernet drops you care about. Then you buy as many APs as you need to cover your floor space, and you install the APs in good locations for APs, and connect them to the nearest Ethernet drop so they get connected to your LAN switch.
The home gateway router at the head of your network doesn't have to be wired-only, but a lot of times the closet where your patch panel is, is not a great place for an AP, so people don't want to use a wireless router in that location because it would be a waste. So they get a wired router instead, and place APs elsewhere in locations that make more sense.
