Firefox has started to do this recently and it's been fantastically informative and helpful. It's the one new browser feature I never really considered wanting/needing before, that's really stood out to me as being incredibly valuable since I've started to see the warnings pop up.
Kinda like how your antivirus tells you about how the formidable threats it saved your ass from today? Or like "did you know your house COULD have been ransacked today, but it didn't happen!!" Now all my users are going to hear that my site is insecure, when nothing at all changed. How long ago did they announce that? I think just a couple months? They should have announced this much sooner. It's going to hit me hard…
In fact you could be proactive and announce to your shared host that for this reason you will be relocating. Let them know there will be a trend of other webmasters relocating for the same reason.
As more and more website features (passwords, geolocation) start requiring HTTPS by browsers we will naturally approach the point where HTTPS is free and ubiquitous, at which point everybody wins.
Also, you've had a one year notice that this was going to happen: https://blog.mozilla.org/tanvi/2016/01/28/no-more-passwords-...