If the network connection is lost due to external circumstances (say your modem crashes) then how would that information propagate from the point of failure to the remote end on an idle connection? Either you actively probe (keepalives) and risk false positives or you wait until you hear again from the other side, risking false negatives.
Observe the line voltage? If it gets cut then you have a problem...
> Either you actively probe (keepalives) and risk false positives
What false positives? Are you thinking there's an adversary on the other side?
Most network links absolutely will detect that the link has gone away; the little LED will turn off and the OS will be informed on both ends of that link.
But one of the link ends is a router, and these are (except for NAT) stateless. The router does not know what TCP connections are currently running through it, so it cannot notify them - until a packet for that link arrives, at which point it can send back an ICMP packet.
A TCP link with no traffic on it does not exist on the intermediate routers.
(Direct contrast to the old telecom ATM protocol, which was circuit switched and required "reservation" of a full set of end-to-end links).
So, except for the links on either of end going down (one end really, if the other is on a “data center” the TCP connection is likely terminated in a “server” with redundant networking) you wouldn't want to have a connection terminated just because a link died.
That's explicitly against the goal of a packed switched network.