Usually when your system can't run a program, there's a symbol of a circle with a line through it on the program's icon when you try to install the program. You can drag and drop the icon to your Applications folder, but when you try to run the program, the system will give you message that you can't because a higher OS number is required.
I've been stuck on Firefox 39 for years and nothing's happened to my system. Depending on how you use the internet, the security fears are excessive. Most individuals aren't targets. Large institutions are, and important individuals, so to speak. Not all of us are under the same risk. We have varying degrees of security needs.
For two years I've used Windows with freeware antivirus and antimalware programs. I've never seen anything especially menacing on my computers. For much of that time I was using Windows XP when so many people were hysterical about dropping it because it was no longer supported.
I can't think of many drawbacks. Some extensions will only work on newer versions of Firefox. The latest version of 1Password requires recent versions of Firefox. So I use an old version of 1Password. Other than what I've mentioned, using older versions of Firefox isn't a big deal.
Opera isn't bad, either, though considering it's owned by the Chinese you might want to avoid it. Although my Mac is ten years old, I was able to run the latest version of Firefox on Mint (on a partition) and it's plenty speedy if you decide to take that route.
OS X 10.6.7
Windows 7 via Boot Camp
iMac Intel Core 2 Duo, 2 GHz (3GB RAM), 17" monitor
Using Apple computers since 1980