Keep in mind the original purpose of the standby ADI was specifically to be the "Umpire." In other words,if one of the two normal ADI's failed or gave suspected erroneous attitude information, an instant time critical comparison was readily available between the standby ADI and the two normal ADI's. In turn, this hopefully would confirm which of the normal ADI's was suspect. Two against one.
Later, adding ILS information to the Standby ADI was icing on the cake. As BraceBrace has mentioned in his post, the earlier first inbound movement of the Localiser on the Standby compared to the old fashioned HSI display and associated FD on the main ADI's was a useful hint that you were closing in on the Localiser.
With loss of all generators in some of the 737 Classics, and thus loss of power to both normal ADI's, that left the pilot with (among other instruments) only the standby ADI which worked off the aircraft battery. That had 30 minutes if you were lucky. Instrument flying using only the Standby ADI really sorted the men from the boys. A skill now universally lost forever for some pilots.