I'd like a mini pc that I can just connect to the HDMI port, where I could watch 4K movies without the need to plug anything else on it except keyboard, mouse, or remote control.
Any recommendation for a mini pc like this or any disadvantage of doing it this way ?
No or limited upgrade paths, but they're relatively cheap for running something like OSMC or LibreELEC. 4k might be a struggle for some of the cheaper ones.
Depending on the TV you may need a short HDMI extension cable because plugging the bulky HDMI connector directly into the tv can be an issue or block other HDMI ports.
Recommend a USB mouse keyboard instead of Bluetooth and maybe a USB extension so the USB mouse/keyboard receiver has a direct line of sight to the couch.
I have yet to find a mini PC that can actually output 4K via the HDMI port without sacrificing refresh rate. Unless you're okay with 30Hz SDR (which might be fine if you don't watch any HFR or HDR content), you'll need a PC with a modern GPU that has HDMI 2.1 support. Like a 3000 or 4000 series Nvidia GPU, for example.
But honestly it's cheaper to just buy a smart TV with Google/Android TV so you can sideload apps and watch whatever you want, without worrying about things like 4K120 and HDR working properly. If your current TV isn't smart, well now's a good time to sell it and upgrade to a nice OLED. November is one of the best times of the year to buy a TV at a good price.