Tear it all out and start over?

You want a full pipe with some sort of wrap material to keep sediment out of of it... if a 'french drain' is the desired result.

https://en.wikipedia.org/wiki/French_drain
https://en.wikipedia.org/wiki/French_drain#/media/File%3AFrench_drain_diagram.jpg

FWIW there can be more than one correct name.

Welcome to real life! :)

Most houses out there were either built well before the internet existed or in an era where dialup was still common. And then WiFi came along and negated most casual benefits of going to the trouble of wiring your home.

If it had become common you would still be coping with different generations of wiring. At one time Ethernet ran primarily on coaxial cable (aka thin net) and there were several generations of twisted pair cabling used for ethernet (cat3, cat4, cat5, cat 5e, cat6).

FWIW, a wired LAN is almost always superior to WiFi and not generally subject to interference from other WiFi and 2.4 / 5 GHz equipment.

It's particularly noticeable where streaming media is involved since momentary interrupts or degradation of service can be very obvious.

On the off-chance that you have wall outlets/panels for wired landline phone service, it might be relatively easy to replace that with ethernet cable.

As others point out, there are methods to run ethernet over coaxial if you happen to have cable to rooms. But that does require an adapter box if you want to connect to a computer or device without a coax port.

In a pinch, powerline networking is also an option.

E.g.

MoCA
https://en.wikipedia.org/wiki/Multimedia_over_Coax_Alliance