GrapheneOS A router's DHCP being filled should not result in any issues.
Absolutely. Anything old/cheap enough to exhibit that sort of misbehavior may well also be old/cheap enough to be remotely exploitable, and probably has poor Wi-Fi performance, so replacing things like that would be good when possible.
I think some people don't have much control over "their" home router. I have a relative whose ISP is Frontier, which covers chunks of the rural U.S. Her router is old enough that she shovels coal into the side of it every morning, figuratively speaking. And I think some apartment buildings provide building-level Wi-Fi instead of individual ISP wiring per-apartment; I wouldn't be surprised if some of those access points were chosen purely based on price.