My understanding is that the earlier rolling code systems are easily defeated and I think this can be done (possibly with stock firmware) using a Flipper Zero.
Prior to that, garage doors had a set of DIP switches (16, or 32, I can't remember). You matched the switch configuration on your opener with the switch configuration on the controller. And as you might imagine, in a typical suburban area about 80% of the garage doors are set to all zeros.
Because the range of the devices was "lucky if you can open the door from the bottom of your driveway", most people didn't notice this. Of course that meant you could open a large number of garage doors by sending the "0" signal for each manufacturer with enough wattage.
Compatible models are made by reverse engineering each individual model's rolling code implementation (in the early days) and making an accessory that had the necessary seed value or other component to allow it to be "paired" with a compatible door head unit. Considering it wasn't uncommon for the higher-end models to charge $150 for an accessory remote, manufacturers had a bit of incentive to roll their own slightly incompatible implementations.
This is from memory and minimal memory at that, but -- late 90s or early 00s, I think, "HomeLink" was created, which basically allowed car manufacturers to integrate a door opener into the car. If you bought a higher-end model, your visor might have the buttons in it. I believe licensing allowed third-parties to easily create fully compatible accessories at that point (pay a fee, get the patent license/datasheets sort of arrangement).
[0] Genie thinks they were first in 1995 but I seem to recall we had a rolling code door installed as early as 1993.
There were also so-called "learning codes" that overlapped substantially with the introduction of rolling codes. Think fixed-code remotes with a random preprogrammed code instead of dip switches. Chamberlain's "billion code" is representative. They have to be paired with the opener receiver in the same way as rolling code remotes.
The largest garage door manufacture in the US uses the Security+ and Security+ 2.0 algorithms that are rolling, but can be fairly trivially decoded to gain the serial number and rolling value of a remote. [0] This is how the flipper zero decodes remotes for playback later.
They use rolling frequencies at least our 2021(?) garage opener does, to retry in the presence of narrow band noise from fcc violating devices. We seem to have neighbors blasting rf in the band that our previous builder installed 2014 model used, because it rarely worked unless super close.
