Let's nip this one in the bud ...
I have used stranded wire with connectors of this type - both 'In-Sure" and manufacturer-supplied, and it's generally not a problem.
You really have to untwist, mangle, and insert at a sharp angle to miss the groove in the clamp. The curved throat of the clamp really does guide the wires into the clamp.
Plus, with OUR wire, at least, the exposed 3/8" or so of stranded wire isn't very flexible at all.
Another forum, a few years back, had all manner of hissy fits thrown by the established members. Even after an Ideal spokesman joined the discussion, they continued to wail "I just don't understand ..." It was more a case of WON"T understand. The factory rep finally gave up, stating: they're listed, so too bad.
I hope we dn't reach that point at ECN. Go out and get some - most parts houses have bins of free samples - and play with them. If you like them, use them. If you don't, use something else.
Also, please drop the 'cheaper' cant. The connectors cost more than even the quality wire nuts (2-color Scotch-lok 2's) that I like to use. If you use the Wagos with the little levers, you can spend as much as 35 cents for each one!