Earlier quoted context omitted.
Token binding was a much better way to do this where you'd bind a cookie to a certain client TLS key. Unfortunately only MS implemented support, and that disappeared when they moved to chromium so I'm guessing it's dead.
Hmm, I'm not convinced it's better—but it depends a lot on your threat model. For preventing malware from using stolen cookies on a botnet, it's reasonable to argue that it's easier for the malware to steal the TLS client cert (which is no less accessible than the cookie jar itself) than it is for the malware to maintain access to the "good" client IP. As silly as IP-binding of sessions is.
From a threat model perspective it is absolutely true that when attacker gains control over the device they could extract the secrets from that said device (they can act as you as well). However token-binding would at least allow for some safeguards against attacks from the application layer (in this case web apps and extensions) in the browser but not against device attacks.