Old-time footage isn't always at 24 fps, but once the film industry standardized hard on 24 fps, not standard film becomes very hard to use correctly, even in a projection environment --- projectors were engineered around 24 fps all the time, and likely can't be adjusted.
Tv of course was fixed at 60 fields per second (or close enough) or 50 in Europe. Even today, a US market tv is going to do terrible things with a 50 fps signal (although I gather EU market tvs work at 50 and 60 and probably 24). If your old-time film was shot at 22.3 fps, you don't have good options to show it, except on a computer with a VRR display, and even then, I don't know if the whole chain will actually be fine with it. Options are: pretend it is 24 fps and it plays a bit fast and you can use your 24fps pipeline; show some frames twice and have nasty judder; interpolate 24 fps from the data you have which is kind of terrible and only recently a real option.