Sure you can get a cheap 4k TV way less, but without a good refresh rate and response time it’s not suitable for gaming. $2k may be high, I’ve not been in the market super recently but it’s certainly wrong to say an entry level 4k Samsung from Costco is suitable for gaming, the response time isn’t close to give the right experience. Same logic as setting graphics to 4k and playing at like 15 fps on a computer on a dog of a GPU.
A computer does need a monitor, and honestly a decent one does cost often upwards of $300, but smaller size without any of the bundled processors etc make it way cheaper than a TV that can do the same.