There is only one true answer to this: "because Apple said so". It's not a meaningful answer simply because Apple's decision was completely arbitrary and not based on any technical deficiency in earlier Mac OS versions whatsoever.
I can tell you why the firmware upgrades require Monterey.
Monterey was the first version of macOS to support centerstage.
Given that the OS that’s inside of the Studio Display literally only does centerstage for the camera (which requires Monterey) and spatial audio (which also requires Monterey), it makes sense that Apple would only put the software update mechanism for the Studio Display in Monterey.
If you hook up a Studio Display to a computer not running Monterey, you don’t have centerstage, and you don’t have spatial audio, basically meaning that the software updates are completely useless to you.
You can still use the display at full resolution as what it was intended for… a display.
You just don’t get the extra bells and whistle‘s that require a modern Mac with Monterey.
By the way, same thing happens with AirPods. And the Apple Watch. And the Apple TV.
To get all the proper Apple integration with these devices, they all have to be updated to the latest firmware. You can’t connect The latest pair of AirPods to a device running iOS 14 and have them work perfectly. They’ll work, they will play sound as intended, but all of the extra bells, whistles and Apple integration requires them to be updated to the latest version of iOS.
It’s no different with the Studio Display. If you connect it to any computer, it will work as a regular display. But if you want all of the exclusive Mac features, you have to be on the latest OS.
If you are not using Monterey, anything this update will provide isn’t going to help you. It’s changing the way that centerstage works, which already isn’t available to you if you’re not on Monterey