Don't know if they still do it in the USA, but about a decade ago Sony XBR TVs were able to OTA update from local PBS stations.
I don't know how useful that was. Most people hook up TVs to cable boxes.
I never hooked up my Sony to an antenna for exactly that reason. There were reports of people being unsatisfied with firmware updates. E.g. the motion interpolation algorithm changed.
This is still used for set-top boxes, at least in Belgium. It happens in the background now, but up until a few years ago when you first got one you'd only see the firmware downloader for an hour or two, with this block diagram where you could follow along: https://i.imgur.com/hh7eWZr.jpg
The worst part about that was if your signal quality wasn't great. You'd see blocks fail, and it'd take ages for them to come up again.
The boxes now ship with usable firmware preloaded, and will update in the background in the first few days usually.
There are several Methods for this - search for OTA...
One of our STB models are still using OTA via DVB-C (I’m in Denmark). Only without the the last few months are we replacing the QAM based SWUPDATE mechanism to an TCP/IP based mechanism (IP is required for using the STB in the first place even though it’s a DVB-C BOX)
Packets in the transport stream include the necessary firmware.