Whenever I've checked my luggage, it has more often than not been at least temporarily misplaced, if not permanently lost. I mean this literally -- more than 50% of the time, something has gone wrong.
I know that I'm a data point of one and am really just unlucky, but regardless, I am quite simply never checking my luggage ever again.
I have to imagine that if carry-ons were banned, and thus the amount of checked baggage increased, more luggage would be lost. Also, more time would presumably be spent waiting on the tarmac while the luggage is loaded, so all this "saved" time would really just amount to more time spent sitting there doing nothing.
So yeah, this suggestion is a hard pass from me.