Finally, from Linksys website:

"However, if your home is already wired with Ethernet cables in every room, some mesh systems can still connect the nodes together using an Ethernet cable to create a whole-home WiFi system. Even using the wired option, you’ll still be able to expand your signal to hard-to-reach areas such as the garage or basement."

So, SOME Mesh systems will do what I want. Which ones? Who knows!
Still, a step forward.