With equivalent time sampling, a 100 MHz bandwidth or even higher is feasible with some inexpensive ADCs at sample rates that an Atmega or similar can handle but this would require implementing an analog trigger and time to digital converter. And do not underestimate the difficulty of 100 MHz signal conditioning; 20 MHz would be difficult enough.
The ADCs in small MCUs use sampling capacitors. Also, the ADC will usually have some series resistance. This effectively forms a low pass filter effectively limiting the bandwidth (I guess well below 100MHz). Though you can get any sort of sample rates with ETS, it still won't have enough bandwidth.
The sampling time constant for typical microcontroller ADCs limits them to somewhere between 10s of kHz and a couple MHz. They can actually be driven faster with a low impedance source but they are not suitable for the reason you identify and more (1) unless an external track-and-hold is used which is feasible (2) but there are easier ways now.
Something like an $3 AD9283 can operate down to 1 MHz while providing a 475MHz input bandwidth. If that sample rate is still too fast, then the parallel output can be decimated. In the worst case, a fast 8-bit external latch (3) and some clocking logic are necessary to capture the output from the fast ADC for the slow microcontroller to digest but these are just a minor addition to the external logic for the time to digital converter necessary for ETS operation.
(1) Microcontroller ADCs would also have too much sampling jitter limiting equivalent time performance. An external track-and-hold solves this problem as well.
(2) A track-and-hold made from a diode sampling bridge can easily get into the 100 to 400 MHz range without being exotic and could feed a microcontroller ADC but it involves a lot more design work than the alternative discussed above. This level of performance is not difficult once you consider a 25 ohm or lower source impedance driving just a couple picofarads through a diode bridge into a JFET or MOSFET gate. Check out the Tektronix 2230 design for a 100 MHz example.
(3) Fast is relative and what is needed is well within the capability of modern easy to use logic families. In the past this was only slightly difficult.