If you remove TV from your service, you wouldn’t need the cable boxes anymore, but you’d lose all the TV channels. No more NBC, CBS, etc. The cable boxes are likely required for TV services. Most cable companies these days digitally encrypt the TV channels. You can’t connect the TV directly to the cable because the TV won’t be able to decrypt the TV signals.
For the non-TV services like YouTube, you’d have your TV connect to the wifi. I’m assuming the TV is already wifi connected since you said there are non-TV products on it.
I’m surprised that your computer connects directly to the cable port on the wall. Are you sure about that? Typically there is a cable modem that provides the internet interface between your computer and the cable, like this:
Computer —ethernet cable----> Cable Modem ----coax cable —> Cable port on the wall
The ethernet cable has connectors that are the clippy connectors like on a phone cord. The coax cables have screw on connectors.