That's exactly what being "on call" is.
You do know that rolling stock have a diagram too? and that it's not just drivers rosters that can't be switched about on a whim? There's the emergency working timetable, the published timetable, drivers diagrams too (diagrams as apposed to rosters) and don't forget the conductors diagrams. You change on you have to change all the others.
It's not always about the driver, the railway will not magically return to normal for the "on call" drivers to operate, the railway is an intricate complex system. You can put all the drivers "on call" in your scenario but is the rolling stock placed "on call" too? Those expensive overpriced units are so awkward as they have been set up for one thing and now you change it at short notice and they are now just sitting in their depots & sidings in the wrong place "on call" so you'll use your "on call" drivers to start moving the units to the right place? but there's a queue to get of the depot and the platforms are already full, the driver for the 10:00 is still stuck at the depot and the only driver available at that time doesn't sign the route. Cancel the 10:00 but we need the platform it's on for the 10:25, can't get the 10:00 of the platform as the sidings are full, can it run as the 10:25? No it's a 12 car emu and the 10:25 needs a DMU............This kind of chaos is avoided by TOCs.
Generally if a strike is called off with 24hours notice or less nothing can be done, with 48 hours notice there is a good chance a nearly normal service can be run, less than 48 hours and its unlikely, TOCS will contingency plans for various scenarios like this based on an emergency timetablewhich could run a much reduced service. But what about the lazy, over paid, selfish, sit on their backside and push buttons drivers? If there is a minimum of 24 hours notice then some will go Spare at their booked hours, some will be allocated modified diagrams, importantly all this will be under existing Ts&C's and agreements. Oddly it is only with these rigid, formal agreements and working practices that the railway can function, everybody knows what can and can't be done and where they stand which is to everybody's advantage.