tcp keep alive don't work when the backend is busy

According to the documentation
https://www.postgresql.org/docs/12/runtime-config-connection.html
A backend must check connection to the client by tcp_keepalive messages. (Config option tcp_keepalives_idle).

But this is don't work if the backend is busy.

Simple example:

psql localhost

set tcp_keepalives_idle=1;
do $$begin loop perform pg_sleep(1);end loop;end;$$;

In other terminal kill -9 the psql on the first terminal.

select * from pg_stat_activity where state='active';
And we will see that the backend is still active and busy.

The more realistic example. In the real code one of the loops, due to bug with asynchronous communication, come to the infinite loop. And occupy a backend and locks for a two week after the client was killed, before we detected this.