I don’t think there are many TVs with both Freeview and Freesat. Plenty with Freeview and free to air satellite though.
That is true, we bought a cheap TV about two years ago in a black Friday deal with Tesco, it had both satellite and terrestrial aerial inputs, however the satellite input only pick up half the programs to our free to air box, I assume either vertical or horizontal not both, but that is a guess. Since I use SkyQ this was not an issue. But one would not want that if you needed the aerial inputs, I only use the HDMI and USB.
But need to explain freesat and free to air. Freesat uses set channel numbers and an electronic program guide (EPG) which gives 7 days and I am told works like the Sky guide in that it gives all channels with out the need to tune into that channel.
Free to air gives not set channel numbers, this can be an advantage, I have mine set so ITV +1 is next to ITV etc. And all those channels often watched together, but you can't use a paper guide as channel 123 means nothing. I use a free to air satellite box in my bedroom, to watch end of programs, so I know where to look for what I want to view, and it can actually have more channels then freesat, however when a program goes off air, or a new program arrives my SkyQ updates, my free to air needs to be rescanned and all the silly programs deleted, there must be around 20 BBC 1's you can get all regions, still on the SkyQ box but all but your region is at end of listing, and porn channels mixed up with the rest, so you spend ages deleting them.
However free to air boxes can use multi-dishes or motorised dishes so you can in son-in-laws case watch Turkish TV. But the boxes which power rotators and/or have multi-inputs are not built into TV's.
Since I don't pay for HD I have more HD channels on free-to-air than SkyQ. But would need to sit on top of TV to really notice the difference.
I use an ICECRYPT STC3250CCIHD set bottom box, and this does receive both terrestrial and satellite so I can watch both and mix and match as I want, with a freesat since channel numbers fixed can't do that, but I would still prefer freesat with a good EPG if given the option.
Freeview is not as good as it claims for the EPG, my Panasonic worked well, my LG would often miss some programs, but today using Moel-y-sant transmitter so freeview just not worth having.