All current versions of Lightroom have some cloud syncing capabilities, but that’s not the same thing as how you purchase/license the software. The “cloud” syncing is a feature that allows you to access your files from other devices. The subscription model is a way for Adobe to constantly deliver new features, support for new cameras, etc. Without the subscription model, you’d have to decide if you wanted each new feature, which you’d have to pay for, but different people would be on different versions and it would make collaboration a nightmare.
Believe it or not, this goes all the way back to the Enron scandal of 2001 and the Sarbanes-Oxley Act of 2002. I know that not everybody is thrilled with the subscription model, but there are significant legal and financial audit reasons behind this. Maybe more detail than you wanted, but there’s more of a backstory than people realize. Here’s an example: https://www.techdirt.com/articles/20070115/163130.shtml