Eero mesh or another solution

Hi 

Just moved to another house. Previous house had networking throughout and I was on fiber optik. Now this house doesn't have networking throughout but does have coax in some spots. Also no fiber optik so on copper. Currently my office is hardwired on the main floor and the modem is in the office. They have managed to get a hardwired network connection downstairs to the wiring closet where the services come in I have attached a switch to be able to attach a wifi extender. So I have 4 of the Wifi extenders. This seems to work well so far. 4 of the TV's are wireless and 2 are hard wired. I haven't had a chance to test the wireless tv boxes, but the signal seems to be strong so don't expect issues. My problem is my son in the basement is in a corner where there is no coax or ethernet. Currently I have a long network cable running to his PC from the switch in the basement. I want to get rid of the cable. My thoughts we perhaps getting the 2 node Eero, plugging it into the switch and then putting the other unit by his desk which is around 25ft and then using the ethernet port to plug into his PC. I don't need the Eero to run the wireless network just to be able to get wired network to his pc. I figure the cost of a good wireless card for his PC would cost about the same. I would appreciate all and any suggestions for the best solution. 

Thanks