I don't see why Nintendo couldn't sell a wireless tv dongle. Plug it into an HDMI port on your TV, then transmit gameplay from Switch Mini to your tv wirelessly. Would be some lag, but not alot if it used 802.11 AC or faster wi-fi for it.
The base model switch needs to do a lot more work when you drop it into the dock, it needs to push almost 4 times as many pixels when you jump from 720p>1080p and you can hear and feel what that does to the unit, do you ever notice how often the Switch in dock has the fans on far more than when it is in handheld mode? the dock is even designed with the slots at the back to vent and direct the airflow in through the bottom of the Switch and out the top, you can also tell how much more work the machine does if you go from docked to handheld play, if it's been in the dock playing for about 20 mins when you take it out the entire system is hot to the touch and that is with the max amount of cooling it could get, so yeah... it wouldn't be comfortable to hold and it would need to run a hell of a lot louder in your hand.
There is one other killing point to this as well, the idea wouldn't be really practical as a handheld device doing it, you would almost certainly need to have the AC cable jacked into the machine. Think about it... if you wanted it to be fully wireless the machine is limited to only having its battery for power, the system never runs at TV output frequency while running on battery, because it wouldn't even last an hour, you ask the gpu to do 4x the work and it's not just taking 4x the power because you now can't rely on the passive cooling anymore so you're running more power for the fans as well as now handling video through the wifi adapter so you've got your wifi portion of the switch running non stop just to display on the TV, would maul the battery.
Oh yeah... that's another issue, you create an adhoc network from device to TV with the Switch's wifi adapter to the TV dongle and good luck playing any online games like Fortnite which is probably what the majority of Switches are being used for. But yeah... there are a number of reasons why Nintendo don't do the thing you suggest here. Pick whichever you want.
Fancy hearing me on an amateur podcast with friends gushing over one of my favourite games? https://youtu.be/1I7JfMMxhf8