Linux

I think part of the reason why the long extension is often preferred is because it's much clearer and it's guaranteed to be supported and decompressed by the respective tools. Even when they don't suppot tar archives, they'll just give you the uncompressed tar in that case.

It's also very common to do that with other extensions (not just .tar) when compressing big files. For example, when archiving logs they'll often be stored as .log.gz, which makes it automatically clear that it's a log file directly compressed with gzip and meant to be examined with tools like zcat and zless to view it.

And in cases like that you really need it to be clear on what data does the gzip stores, since it does not keep metadata about the file so you might not be able to get back the original name/extension of the file if you rename the gz file.