It's a common misconception that routers handle TCP. They strictly handle only the IP headers (and lower-level headers).
The TCP protocol is implemented only by endpoints, at least in principle.
It's the "security appliances", also known as "middleboxes" that are the problem. Think web proxies, antimalware scanners, firewalls, and inline IDS systems.
These things are the bane of the Internet, because they ossify protocols, blocking any further development.
Although what a consumer considers a "router" is actually a middlebox doing a bunch of things and does care. (CG-NAT in provider networks is probably another example of a common problematic middlebox)
The TCP protocol is implemented only by endpoints, at least in principle.
It's the "security appliances", also known as "middleboxes" that are the problem. Think web proxies, antimalware scanners, firewalls, and inline IDS systems.
These things are the bane of the Internet, because they ossify protocols, blocking any further development.