The tiny SBY's are still there but no-one looks at them
For the very reason you stated (no one looks at 'em) I have always had the standby ADI ILS switched on for all approaches where the ILS is available on the landing runway - visual or not. It is not so much as a back up in case of sudden double generator failure (extremely remote) but to keep those vital instruments incorporated into the normal day by day instrument scan.
In the simulator, it is an interesting exercise to train new pilots what happens if a lightning strike late in the take off roll disables both engine driven generators simultaneously. After all we train for double generator failure as part of the type rating course and that can happen equally likely in flight or on the runway.
Lots of caution lights, spurious warnings including take off configuration and importantly, loss of half the wheel brakes. A reject at that point could cause an over-run on a limiting runway. The climb away on the standby ADI involves not only manual stabiliser trim but it is all too easy to over-speed the flaps and LED as the flap indicator is inoperative. That is because the tiny pitch indications on the standby ADI makes it difficult to see and sometimes even misinterpret the pitch angle numbers and what you thought was 15 degrees body angle after lift off can very easily be 25 degrees real angle. Been there-done that in the simulator several times. And of course with double generator failure the pilot is back to real raw data with a vengeance.
All is not lost for the competent pilot, however. Adjust the trusty bi-focals, set the desired the pitch angle, and ensure desired thrust set for climb or what is appropriate for the occasion, which is just what you would do in any aircraft including a Cessna 172..
Finally, one has to be especially careful to remember the localiser indication on the standby ADI in the 737 Classic, works in reverse if tracking away from the ILS.