Why did Wondows 10 install destroy Office 2013?

Every few years, they bring out a new buy office 2013 standard suite, not because the old one doesn't work, but because they need to make everyone's software obsolete. The last time they did this, I reluctantly bought Office 2013, which offered no discernable improvements but took up more disk space and wiped out my 8000 contacts in the install.

Last week, I installed "free" Windows 10, and I started getting a message that my Office 2013 wasn't registered; it demanded my product key, which I haven't seen for a couple years -- but which I obviously had, since it's been working without any such warnings for years.

I called Microsoft, and they offered to sell me a new product key for a clipped-wing version of cheap office 2016 professional plus for a hundred bucks, or a complete Office 2016 suite for $249. I called their tech support; they pointed out that they don't keep my product key -- it's in the "Terms and Conditions" (no doubt on page 488 or something -- but what can you do, anyway?). Well, Office 2013's search feature can't find the email that has the key, so...