The Nintendo switch doesn't run most games at "1080p", in fact the game DOOM drops down to about 640p or so.
The 1080p output is simply whatever the game resolution is, then quickly scaled to 1080p and output via the HDMI connection when docked or 720p on the screen (or just 720p when docked I'd have to investigate that.. wouldn't make a difference).
4K and 1080p should look exactly the same within the limits of whatever difference in video processing is done to the 1080p signal, but that won't be significant likely (except to possibly add a lot of LAG due to the HDTV's processing time so you want a "gaming mode" type option for the HDMI input, or know that the HDMI input is low latency (i.e. under 40ms).
So...
Not sure why you say...