I have some very interesting info to report on this exact problem. This is a complicated description so I hope you can follow. The new piece of info comes at the end.
I have been troubleshooting this issue on my Mac Pro 5,1 2010 all day long. It was helpful to see that designating a different screen as the main screen "solved" the problem, except that meant my screens (3 of them - a 24 inch Dell, a 24 inch Samsung, and a 20 inch Samsung) were not in the configuration I wanted them to be in. My Dell had been the main screen with the 24 inch Samsung on a shelf right above it and the 20 inch Samsung to the left of the 24 inch dell. However I very purposely had all 3 screens arranged horizontally in System Prefs because I didn't like trying to click on menus (File, Edit, etc) at the top of my main screen and accidentally ending up with the mouse up on the Samsung on the shelf above because I moved too quickly. So I pretended the 24 inch Samsung was to the left of my 20 inch Samsung -- it meant having to move my mouse all the way to the left to get to it instead of up, but was worth the tradeoff. However in this configuration, I found out that screen control only worked on 1 screen at a time from any other computer.
So this thread caused me to try (without physically moving anything yet) to make my 24 inch Samsung on the top shelf the main screen, and voila -- screen sharing across all 3 screens from other computers started working again. So I figured it was something about the brand of screen itself and meant that I needed to physically take apart my system and put the Samsung on the bottom shelf and the Dell on the top but leave the 20 inch Samsung where it was on the left. So I did all that and, of course, had to re-configure the display arrangement so my computer knew where everything was again -- and Screen Sharing was NOT working again after all of that moving things around!
Long story short, I realized that it wasn't which screen was designated as the "main" screen that causes this bug. It was the arrangement layout itself!! I played around with it and if I went back to telling the computer that my main 24 inch screen was in front of me, 20 inch screen was to the left of that, and my 2nd 24 inch screen was directly above my main 24 inch screen, screen sharing worked just fine from other computers!! I never had to physically swap the Samsung and the Dell in the first place! I just had to NOT use a side-by-side completely horizontal arrangement configuration. Which, unfortunately, means I once again have to deal with it being too easy to accidentally end up with my cursor on the top screen -- but at least I know what the heck was causing it now.
Definitely a bug and I experience this in Yosemite and Sierra but NOT Mavericks. So it started in Yosemite.
Hope this finding at least helps others.
And no, I do not want to put my top screen to the right of my main screen. I have something else there.