We are talking about low level drivers. It is not like you had an application in your Applications folder, and it disappeared after an OS update. That doesn't happen.
Things like DisplayLink tie into the OS at a very low level in order to provide their functionality, and hence they often need to be updated when a new OS comes along.
There is one other factor at play, in the perception that a new OS "breaks" things. There can and have been bugs, but, for the most part, problems come down to old stuff like drivers, system extensions, launch daemons, sometimes stuff that the user installed while running, say, El Capitan. It is so easy to upgrade in place that users tend to do so for many years, OS after OS, and mac after mac. After a while, it is almost inevitable that something will break, and then of course people blame Apple, rather than their own lack of due diligence. It is recommendable that at every major OS, you do a clean install, migrate your accounts, and then install the applications fresh. This way you won't end up with, say, Perian (which was discontinued some eight years ago), or other old stuff breaking your system. [Note: I am using Perian just as an example; it was a very useful piece of software back in the day; the developers clearly stated it had been discontinued, and it cease to work several iterations of the OS ago, and yet... I have seen people still having it in their systems in 2022. The same with, say, Silverlight, or even Flash....]