It does do that and it's pretty neat, if you have one of the very few modern turboprops or small jets that have G3000s & auto throttle to support it.
Airliners don't have this, but they have a 2nd pilot. A real-world activation needs a single-pilot operation where they're incapacitated, in one of the maybe few hundred nice-but-not-too-nice private planes it's equipped in, and a passenger is there to push it.
But this is all still largely using the current magenta line AP system, and that's how it's verifiable and certifiable. There's still no cameras or vision or AI deciding things, there are a few new bits of relatively simple standalone steps combined to get a good result.
- Pick a new magenta line to an airport (like pressing NRST Enter Enter if you have filtering set to only suitable fields)
- Pick a vertical path that intersects with the runway (Load a straight-in visual approach from the database)
- Ensure that line doesn't hit anything in the terrain/obstacle database. (Terrain warning system has all this info, not sure how it changes the plan if there is a conflict. This is probably the hardest part, with an actual decision to make).
- Look up the tower frequency in DB and broadcast messages. As you said it's telling and not asking/listening.
- Other humans know to get out of the way because this IS what's going to happen. This is normal, an emergency aircraft gets whatever it wants.
- Standard AP and autothrottle flies the newly prescribed path.
- The radio altimeter lets it know when to flare.
- Wheel weight sensors let it know to apply the brakes.
- The airport helps people out and tows the plane away, because it doesn't know how to taxi.
There's also "auto glide" on the more accessible G3x suite for planes that aren't necessarily $3m+. That will do most of the same stuff and get you almost, but not all the way, to the ground in front of a runway automatically.