I had a 1080p monitor and it looked slightly pixelated. I bought the LG Ultrafine 4k display and it looks great. I asked my work to buy me a monitor for the office and they offered a 1080p monitor. I am a web and graphic designer so it looking good is important to me. I also noticed that the native display is 2560 x 1600 which isn't 4k. Am I going to have to convince them to get a cheaper 4k monitor? I have a 2017 Macbook Pro Touchbar.
Yes. You will have to convince them that you need the proper tool for your assigned task, one that offers 3840 x 2160 or 4096 x 2160 pixels.
You also need your display to be flexible enough to emulate the different resolutions your end-user may have.
The real issue is PPI, that is resolution dividing by size (both in diagonal). The larger the display is, the higher resolution you will need.
Also the distance between eye and monitor is important, but that does not generally change much.