The bottom line is that you can ignore updates, but the longer you go the riskier it becomes. It is not just a security thing. If you share things with other Apple devices, if they get updated but not your iPad the shared features may fail. You mentioned that you wasted 15 minutes trying to fix airdrop. That is a drop in the bucket compared to fixing windows issues, or isolating incompatible device issues due to IOS or MacOS version incompatibilities. These kinds of things can take hours. The more you get out of a "standard" configuration the more difficult it is to isolate and fix problems, and the more time it is going to take to fix them. When you call Apple Support with a problem, they usually will make sure that you are running the latest version before they do anything, since it has the latest bug fixes.
The reality is that eventually you will have to update, whether you like it or not. When you replace the iPad with a new version it will likely not work with earlier versions of the software. Or you install the latest MacOS on your MacMini to get a new feature, and it breaks Airdrop to your iPhone. Rather than having many major issues upgrading to a version 2 releases away, attending to these issues as new releases are made means you can fix things in small bites, not a huge gulp.
You are right on the fact that you cannot use an older version of iOS in newer iPads, but backups are compatible - barring 32-bit apps - so there shouldn't be any problem.
I had one problem, for example, regarding incompatibility: A friend had an iPad on iOS 9, mine was on iOS 7. We needed to transfer a Pages document to my iPad. My iPad wouldn't open it "Update Pages to open this document". "Pages requires iOS 9.0 or later". We could not transfer it. I had to seek a third party solution.
As I have always said, the largest issue I have (now running iOS 9.3.4 on a 9.7 iPad Pro) is app compatibility.
But that's worth the hassle. My iPad works perfectly, and barring hardware issues, will continue to do so. That higher security (pun intended) is worth it.
Yes, Apple always instructs to update. I had to airdrop something from my iPad to my 2015 Retina MacBook Pro, running OS X El Capitan (I refuse to update based on the same principles). Apple told me to update the iPad, as I contacted them because the Mac AirDrop wasn't detecting my iPad. I refused. It fixed itself a few days later. I don't know why.
I had a storage issue, too, where my storage was eating itself up. Apple told me to delete everything, update, create a new account, and transfer everything. I refused. I sought help in MacRumors, and the issue was fixed with a very simple tip: The storage are undeleted Time Machine backups kept on the computer. Turn Time Machine on and off, and you'll fix it. Apple never told me that. They went the hard way immediately.
As an end result, my iPad is working perfectly, and barring a few stupid apps I wanted to install and didn't need, it has everything I need and want.
