Do any aircraft have a "self-contained ILS"?
Approaches guided by GPS are called RNAV; it can provide both lateral and vertical guidance, in some cases to the same precision as ILS Cat I, without need for a radar altimeter--which is not standard equipment. (There are also non-GPS ways of using RNAV, which are mainly used by older airliners that haven't been upgraded yet.)

Note that standard GPS has accuracy of 100m; SBAS (aka WAAS) gets that down to 7.6m.  Both are standard in aviation GPS units these days, and GBAS (aka LAAS) will eventually get that down even further.

There are already three times as many RNAV approaches as there are ILS approaches with more appearing every day, and most aircraft are now equipped to use them or probably will be soon. IOW, the essence of what you propose is already here.

Instrument approaches do have to be pre-planned to ensure obstacle and terrain clearance, so airplanes can generally only use them to land at airports. (The rules are different for rotorcraft, and that's generally what you'd use for rescue, but I'll have to leave the specifics to someone else.)

Many large aircraft carry weather radar, but it's too heavy for light aircraft; both can use satellite weather data services, in addition to getting weather updates via radio the traditional way.