Time machine kicks the shit out of whatever that horrible thing with the umbrella logo that came before it was. I, too, have spent a Very Bad Weekend doing Time Machine archaeology and you're right, it truly, truly sucks. But it's integrated into the OS, it's super-easy to set up, it's super-easy to work with - when it works - and when it doesn't work, Apple will happily sell you more hardware. I've got four computers talking to the Synology as a Time Machine target. It actually works pretty goddamn well. On the other hand, configuring Macrium Reflect on Windows 10 was a chore and a half. So I get what you're saying. But the fact of the matter is I've got Time Machine working across four operating systems and while I'm certain you could do it slicker and faster and lighter, I can't.
And that's of course why they're successful, because if you asked me how to handle your backups I wouldn't have an answer that didn't start "write a shell script that ..." and there are plenty of people with enough important data that "periodically make a tarball and stick it somewhere safe" isn't good enough to who "write a shell script that ..." might as well be "go fuck yourself." But building Rube Goldberg machines so your users don't have to care what's happening risks failing spectacularly for anyone doing something a little unusual, and eventually collapses under its own weight so you have to start from scratch. Which might also be good for the business, witness the frequency of new Windows versions, but is a pain in the ass for both users and developers.
This, I believe, is why Carbon Copy Cloner exists. It allows you to do "time machine" shit with a great deal of flexibility and configurability and I suspect Mike and Rob bailed on Apple when it became clear that Time Machine was going to do that one thing and that one thing only and when it stopped working Apple was going to say "oh well." Something to think about: back when I used to design AV systems for corporate boardrooms and the like, fully half our budget was in the control system. Something else to think about: for twenty years, when asked for recommendations on stereo equipment and the like, I will say "go play with a lot of them and choose the one with the remote you understand the best." It took me a while to get there. As an engineer it's annoying as fuck that "how the morons do it" matters more than "what it can do" but years of experience bears out this simple observation: If users can figure out how to do it, they'll do it. If they can't, they won't. There is no point in building functionality that users won't use, thus there is no point in making Time Machine anything other than a one-trick pony. THAT is the genius of Time Machine - it's a set'n'forget backup system that your mother can configure without consulting the Internet. It's also the downfall of Time Machine - when it stops working you have to go deep into the command line. BUT since it's "backup", and since the majority of users have none, having one that burps and dies every nine months is a vast improvement. After all, most people don't use their time machine backups at all. I've got five of them and I had to crack into one, once, in the past five years. I think that's the defining line between Steve Jobs and Tim Cook - Steve Jobs loved design, but he loved UX more. Tim Cook loves design and figures that enough skeuomorphism will channel his users into appropriate behavior.