Couple things,
If you put an LCD on the board you're going to need power (usb if you use a Pi model) and hdmi, you can't just use USB, that means 3 cables, one of them very large, going to your keyboard. There are small lcd's that wire into a board but they have extremely limited function, I.E. you can't pull much if any info from the computer without writing custom drivers and adding more computing power to the keyboard. Not going to happen with just QMK and a Teensy or cheap Pro Micro. Also, depending on your OS ((I.E. Windows), you also may have to buy software (such as Aida64?) to get those values into a form you can export to a keyboard.
A screen on your board is out of your line of vision, it means looking quite a ways down to get just a small bit of info. Worse, it's fixed, sure you can make it hinged but it's always positioned based on your keyboard, or removed with your keyboard. On many games I rotate my board about 30 degrees for less wrist strain, that means the screen would be rotated 30 degrees.
You're also kind of stuck.
Burned up a screen, pray you can find a replacement that fits? Want to change something? How about wanting a new board or yours died? It's built in. You're putting all your eggs in one basket and kind of limiting your upgrade path. Keep your keyboard just a keyboard, it leaves you free to change your keyboard all you want without being stuck. In the end I put mine in a dock attached to my monitor shelf. I also added a USB dock, remote power switch and later a screw tray... It's up higher (easier to see), I can relocate it, no thick cables and when I got bored of it I could remove it and not effect my keyboard.
Also there's problems...
Most of these little Pi screens don't go into a true sleep mode if they have power, they go into super bright blue. So every time the computer goes into sleep or standby your screen goes into hyper blue mode. Some boards will let you turn USB on and off, so will some hubs, but not all, and it means an extra step if it's a manual switch.
Some GPUs freak out with more than 2 screens, particularly Intel. I have dual screens and then I had a tiny third mounted in a dock, when using onboard gpu NONE of the screens worked during boot until the OS loaded drivers. No amount of bios tweaking would fix it. This is because some ports on Intel are shared, I.E. you may have 3 ports; 2 Displayport (DP), 1 HDMI but one DP and the HDMI are shared so only one can be used at boot. My system also had a USB C port and if I used a type-c to HDMI but when doing this the small screen only worked once booted, but at least I could see my boot info. Using a gaming GPU eliminates this issue, but you still have the power issue.
Basically, you can get more functionality and longer life out of a hub with a screen, than a keyboard with a screen.
Like I said, I added a screw tray (with usb stick and SD storage) to my hub later, I wouldn't want that on my keyboard, same with power button or a USB hub, but it all works great as a dock and it never interferes with my keyboard.
Pics of mine: