For NEMA 5-15: Better outlets do help, but do not eliminate the problem: A tighter friction fit is still a friction fit, and given enough wiggling they still tend to work themselves loose -- just on a longer timescale.
A connector with a positive snap-action would seem better: It is either snapped tightly into place, where it is connected and it works. Or it is unsnapped, where it is electrically disconnected and free to fall out completely. USB C seems to get this part right, as an example; good versions of the C7 ("mickey mouse") power connector seen on many laptops and boomboxes of yore also seem to get at least part of it right.
Anyhow, I don't think it can happen with a new combined outlet that preserves 5-15P compabibility, so...
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Your combined outlet idea is neat, but it increases the minimum size by 50% and that increase may require new boxes, and definitely requires new coverplates.
I'm thinking something more like this arrangement:
| o |
U
Key: | is existing 5-15-style blade opening, U is existing 5-15 ground, and o is the new terminal on the other hot leg of split-phase.
The new terminal can be a blade, but a square or rectangular cross-section seems better: It's still flat for ease of making good contact, but it's also strong in more than one direction. Having a shape for that hole that is incompatible with existing blades also helps prevent Curious Little Jimmy from bodging a 5-15P into the wrong holes and torching appliances by applying twice their expected voltage.
It preserves 5-15P compatibility, does not necessarily increase the space used inside of a box, and fits behind the existing (and vast) array of cover plates. Grounding remains optional, and polarization and remains optional for non-grounded things (and both are determined by the plug end, not the outlet end, just as today).
The ground terminals always face the "outside", which is perhaps safer, and the inverted outlet
Still to sort:
Tamper resistance mechanism. The NEC requires that mechanism in many cases, these days, and universal application requires NEC compliance.
Also compatibility with existing wiring. One advantage of using a single-purpose outlet like 6-20R or even L6-20R is that existing wiring can (in some cases) be re-used by re-identifying (eg) the white wire for use as a hot leg, and this can speed adoption in some existing dwellings. But both of the layouts we've drawn have a neutral terminal on their face and invite the insertion of 120V plugs, even if they won't work.