I certainly don't see anything that would make a single edge fixed blade less than 5.5 inches illegal to carry under state law, regardless of the handle configuration. My two cents worth.
I would be interested to hear if anyone can actually get their local DA or judge to commit in advance as to what might or might not be legal unless a) it is blindingly obvious (like murder), or b) you've been buddies since 3rd grade and you catch him in a weak moment. I think the more likely answer is they will tell you to consult an attorney of your choice. BTDT. But if anyone succeeds, would love to hear about it.
I certainly do not see a push knife as an "inferior design." Inferior for peeling and dicing in the kitchen perhaps, but for bad-breath distance last-ditch wrastlin' around fighting, it has some advantages, I think. As an overall carryin' around and fightin' knife, I would prefer a traditional fixed blade of as many inches as I can reasonably carry (and I do), but I think the push knife's advantages are a) it is small and easily concealed in places that make it handy to reach, and b) once in your hand it is harder for your opponent to disarm you (than a regular fixed or folder), and harder for you to drop on your own either by accident or from being struck. You can open your hand and still keep the knife clenched between fingers, for example. And any blade is a big jump up from fingernails.
It is kind of like the snubby of knives; not really the best "only" choice unless there is nothing else you can carry, but in its niche, it is excellent.
The TDI seems to be somewhat of an attempt to cross the fixed blade with a push knife; I have never practiced with one, but so far I think I would prefer to stick with a traditional knife or a push knife -- or best of all, both.

But they are very popular and I will have to try one out some time.
If you like push knives, you may like this as well:
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