What do you mean by 2K resolution? A lot of people use that term incorrectly.
At 1080p a lot of games will not fully utilize the 1080 Ti at 2K resolutions unless you use SDR (super dynamic resolution) to render the game at a higher resolution (looks slightly better, but not as good as a real higher resolution screen).
So, it wouldn't be an entire waste. What is the refresh rate of your monitor? What is your current GPU?