This is an idea that was mentioned in #1278 and could be part of the #1839 meta-issue...
So the idea is basically to have an additional "Place in layout" action available in the drop-button in the "Operations" column (mockup):

...this would pop up a dialog asking which layout to add the block to, and upon selecting a layout, would redirect to the "Manage blocks" page for the selected layout, perhaps with a "Select region" prompt?
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OMG thank u... you are amazing.
Hiding Blocks for Small Screens
I use a similar module (Tocbot) which uses the same library, but the implementation is different. This is what I use to target the block: @media (max-width: 47.99em) { .js-toc-block.is-...
Hiding Blocks for Small Screens
So the implication is that another module is causing the trouble. Now for the slow process of elimination... Sounds plausible. And good luck with digging...
How to troubleshoot interactive image cropping modules?