Well it is not that I want to reinstall windows 10. I have done that a dozen times.
A few facts.
Windows looks at your BIOS Serial Number, and it it is an OEM based system, then yes it can reinstall the OEM version of your windows 10 and pick up the Key Number. However, you have to be using the OEM version which was either created from your computer,
by burning a DVD recovery media, or is in a hidden partition on your computer, which uses a function key or combination to restore your computer to factory new again during boot process.
During the install of windows 10 it slipstreams the Product ID (Key Number) into the install. The hidden restore does that. You will lose all installed beyond factory software.
But as you said as long as you had backed up your system. There is no limit on how many times you can install windows 10 on the same machine, but there is a limit to how many times you can install windows 10 on different machines using the same key number.
It depends on the licensing, that you purchased. Microsoft maintains a list of legitimate key numbers, in their database. And they know if it is being used on more than 1 machine. OEM links your COA that is no longer applied to OEM computers.
Used to be but they tend to rub off or people would remove and lose them so they just stopped. A purchased NON OEM windows 10 typically allows 1-3 computers you can install it on.
That is not based on hardware. But the OEM version can only apply to your computer for use on that machine only. If someone stole your key number it would not function, because it is as you say tied to the BIOS Serial number of your computer.
Sadly Windows 7 did come with Backup Software, although it was slow and cumbersome, but it did work. Windows 10 they removed that. So you need to get 3rd party software to get past that.
2 choices that I use, are Acronis or Macrium Reflect. The latter having a free version, but if you go to Seagate, you can get a free version of Acronis that comes with the Seagate Tools software. In fact the Seagate Tools version, is fully compatible with
any computer, and is actually very EASY to use, and runs in the background while your using Windows 10. So you can backup your entire C drive or entire hard drive, to an external drive, or second hard drive, and restore both just files and folders, or the
entire computer, using Rescue Media that it will create for you, use either a flash drive or DVD burner to create.
I understand that re-installing windows 10 might fix the problem, but in reality it just means that I get to rebuild my world back up again, and time consuming beyond belief.
Now gettng back to the issue, the real hangup I have with windows update, which has existed since it became integrated into Windows with Windows Vista, is that it does not work as it should. Yes it is stated that if an update fails it is supposed to automatically
reinstall it. But the log keeps showing the failed ones, instead of removing the failed ones, and showing you that they got done at a later time.
And it seems I still get failed over and over updates, no matter and so eventually maybe they release a Cumulative that like the SoftPacs, does fix the failed ones.
The biggest reason why you cannot just reinstall software, and have it pick up your old information, is that of the registry. Some programs you can migrate the User folder back and retain from where you left off. But some you cannot.
Again it will vary.
Lastly there is a free program called WSUS which downloads, and gives you an Offline Installer. However Microsoft limits the updates it can gather. It is really useful for Windows 7, but does not give you all of the updates. It does the updating in a much
different way. It does use less system resources, and also works by running the update portion to any computer, so it is effective to some degree. And of course it shows you in a log file, what updates it was able to process and seldom fails.
Finally like everyone else I find that Microsoft Support, is actually very poor, in that most responses to a specific problem, are given a pat answer, that seems to be coming from a standard list of responses to everything. It seems to be outsourced, in
that regard.