Flight service remotes

Flight service has a remote radio site somewhere in our area.
When contacting them via the remote, the specialists want you
to state you're calling on that frequency. If you don't, they
seemingly have the remote transmitter off and you won't hear
their reply. If you call them again without the frequency,
they'll turn on the remote and sound irritated that you didn't
tell them which frequency you're using.

Is the FAA saving money for electricity by switching the remote
transmitter on only when it's actually being used? Wouldn't it
be better to leave it on all the time so the users of the
remote will have some idea as to whether the specialist is
talking to someone else on a different frequency?

AFAIK, ATC has the controllers talking on all the frequencies
that any one controller may be handling at any given time.
That's why we hear one side of comm with military pilots on
the UHF freqs, for instance.