The problem is, the Amiga has a vast library of software (primarily games and demoscene productions) that boots off directly from a floppy and employs custom disk-loading routines which start off from the bootblock. This was done back in the days when an HDD was seen as an expensive extra.

At the beginning, the assumption was that most people interested in games would be using the cheaper Amigas, possibly with no HDD, and they would only have a floppy drive or two at their disposal. (The early Amiga models did not come with HDDs as standard.) Custom trackloading routines were also used for copy protection and performance reasons: reading raw data off the tracks and copying it to the memory is faster than if you load the same data by means of files and a filesystem. And, of course, just powering on the machine and inserting a floppy was an intuitive, simple-to-use interface for starting games; akin to the cartridges on the game consoles.

(The AmigaOS itself, and software normally running under it - tools and utilities, shareware and productivity titles - were always made to be HDD-installable and they utilized a normal filesystem from the beginning, of course. But there's a staggering amount of old games and demos that go with their custom raw disk format and a custom trackloader.)

Now, WHDLoad - which is essentially a binary patch library for various Amiga software titles - remedies that problem for some titles, by making such older releases HDD-installable and their fixing potential compatibility problems with the newer Amigas and newer AmigaOS versions. The patches might even clean up some badly written software, making them allocate memory properly and even adding clean-up and "quit to the OS" functions, instead of requiring a reboot of the machine after you're done with the game. This is all good, and a great accomplishment, but WHDLoad needs a separate driver (called a "slave" in WHDLoad terms) written for each piece of software it "supports". So it's not a universal solution.

Also, since the Amiga floppy disk drive controller is very flexible in how it can be programmed, and the AmigaOS normally uses a floppy format that is incompatible, on the sector level, with standard PC floppy controllers (formatting 880 KB on a DD floppy and 1760 KB on an HD floppy), generic products such as the PLR Electronics 3 ½ floppy drive to USB flash drive reader are not likely to work on the Amiga.

There is an interesting hobbyist DIY hardware project called A Universal Floppy Disk Drive Emulator, however, which aims at making floppy drives redundant on Amigas and many other devices, by replacing them with a floppy disk drive emulator. It is basically the same idea as with the above-mentioned PLR Electronics product, but the project is hobbyist-driven and open, and also guaranteed to be compatible with the low-level sector format that the Amiga normally uses. You can find the schematics and the required software on the linked website.

Are you sure those weren't actually Amigas? This page has some information - even photos and screenshots - about the usage of the Commodore Amiga at NASA.

That hasn't been true since the introduction of the OpenDML AVI format, aka AVI 2.0, and the transition to DirectShow APIs (as opposed to the old "Video for Windows" subsystem.) This transition happened, for the most part, somewhere around the beginning of the decade.