There are a few reasons that a game might have impossible trophies. Some of the most common reasons include:
Every PlayStation game has an internal ID that is either of the form "CUSA#####" (for PlayStation 4 games) or "PPSA#####" (for PlayStation 5 games). This code determines whether or not DLC and save files are compatible with each other (this is usually not something that anyone needs to worry about, but it is important to know when buying different versions of a game or games from other regions).
For example, in North America the base version of The Witcher 3 has CUSA code "CUSA00527", while the Complete Edition of The Witcher 3 has CUSA code "CUSA05725". Since these codes are different from each other, you cannot use a save file from the base version of the game with the Complete Edition of the game. On the other hand, the base version and Definitive Edition of Shadow of the Tomb Riader both have CUSA code "CUSA10938", so their save files are compatible with each other.
CUSA and PPSA codes are usually the same within North America, within Europe, and within Asia (but different between them). So, for example, if you buy a game in Canada, the United States, and Ireland, then save files between the Canadian and American versions of the game will usually be compatible with each other, whereas save files from the Irish version will not be compatible with either of the others. There are exceptions, however – games sold in Australia usually have the same CUSA code as their counterparts sold in Europe, for example, but the Australian version of Saints Row 4 has a different CUSA code than any other region.
When buying games digitally, you can see their CUSA code or PPSA code under "Details" on their PlatPrices product page. When buying games physically, you can see their CUSA code or PPSA code at the bottom of the case's spine (see the photo below), and also on the disc itself.
When a game is delisted from the PlayStation store, sometimes its DLC entries are not. In these cases, the DLC is left "dangling" on the store, not corresponding to any version of the base game that can be purchased digitally. However, the DLC will still work with any copies of base game that were purchased prior to de-listing, and with disc-based versions of the base game.