The problem is that few printers support _all_ of these standards. Postscript, for example, is surprisingly complex to implement in practice, which leads to a lot of inexpensive network printers actually lacking postscript support. Further, printers are very slow at rasterizing, and so while support for PDF rasterization is very common you probably don't want to use it. You can easily see a minute per page for printing modest PDFs. In-printer PDF rasterization is also of very uneven quality, and I have seen issues like completely broken kerning in documents due to the printer's poor handling of embedded fonts.
One of the key functions of something like CUPS is to address this problem: CUPS standardizes the format of all printed documents to something that is well-supported by the printer, and performs much of the rasterization ahead of time on the much faster print server. This saves time and improves reliability since you don't need to figure out if a given document is supported by the printer. For most printers these days some variant of PCL is the preferred language for jobs, as it's simpler and easier to implement than Postscript. It also presents fewer security concerns.
Of course the other major problem CUPS solves is the management of the queue, including across multiple users. That's an important feature but not one that matters in a lot of home situations. That said, if you don't use a printing system you can and will run into annoying situations where you cannot print a document because you are waiting for the previous one to complete sending, which often gets blocked on the printer's memory space or rasterization.