Separate from any speed limitations, old and inexpensive routers tend to accumulate known and unknown unpatched security issues. Firmware updates tend to fade in frequency and eventually become unavailable.

Hacks and botnet infestations of Internet connected devices can be hard to detect after they have succeeded. Absence of router updates can allow them to remain embedded.

Straight up bugs and implementation errors can bedevil a home network for the lifetime of the old router.