Why you don't actually own any Amazon Prime Video content
A legal case filed earlier this year came to a head in October, solidifying Amazon's claims. The case saw Amazon Prime Video user Amanda Caudel sue the streaming content provider for "unfair competition and false advertising" because Prime Video purchase access can be revoked at any time. Amazon argued that their User Agreement makes clear that an Amazon Prime Video purchase isn't the same as ownership.
You don't own streaming content
"The most relevant agreement here — the Prime Video Terms of Use — is presented to consumers every time they buy digital content on Amazon Prime Video," wrote Amazon attorney David Biderman. The terms, said Biderman, "expressly state that purchasers obtain only a limited license to view video content and that purchased content may become unavailable due to provider license restriction or other reasons."
You'll be hard pressed to find a company which guarantees eternal ownership and access to digital-only content here in the year 2020. Paying for a subscription to Netflix doesn't guarantee you access to every movie and/or TV show available for streaming forever. Paying for access to an online-dependent app doesn't guarantee access without end.
It is by the nature of required internet access and limited licensing that streaming content cannot be owned indefinitely. As it is with Amazon's content, so too is it true that any time you "buy" a piece of streaming content, you only really "buy" a limited-time license.
You can find more information on the legal case noted above with the United States District Court, Eastern District of California, Sacramento Division with AMANDA CAUDEL v. AMAZON.COM, INC., Case No. 2:20-cv-00848-KJM-
Should you buy discs instead?
You should not necessarily just default to hardware-based content just because it's impossible to own an eternal license and access to streaming content. We're living in an age of access, and it's in the best interest of each content provider to provide value to the user. If you're the sort of person that enjoys the idea that you've got guaranteed access to your content forever, buying physical discs (or the equivalent) might still be your best option.
My own personal default is paying for a subscription to services like Hulu, watching content when it's available, then moving on to whatever's new when it's released. When I find a show or movie I enjoy enough to watch time after time, I purchase a Blu-ray or DVD.
I learned my lesson when I started buying digital movies a decade ago: Services end, content is lost. You're fresh out of (legal) luck!