The republican trick is to make sure everything is "means tested".
It's also to make everyone work for everything unless they can prove that they shouldn't have to, and then they make determinations about who can or cannot prove it without medical qualifications.
Yes you can buy lobster using EBT, but so few you will starve, and direct knowledge of this would defeat all the stories.
There is a broad spectrum of opinion on what SNAP should be for, and who should get what kind of food aid, and how much. The intent of the program from a federal perspective is to provide supplementary food, it's right in the name, which implies that they think that everyone should be dependent upon either labor or literal charity for at least some of their food. Some state do their utmost to avoid handing out food aid, while others do their best to provide it. Recalcitrance in relation to feeding people is unexplainable from an economic standpoint because the money benefits everyone in the state, and it seems like it should be difficult to justify for people who commonly like to cite Jesus as their reason for voting one way or another, but it does exist.
Some people feel, as you invoke, that one should not be able to purchase luxury food items or even unhealthy ones with food aid. Indeed, there is a program for pregnant and nursing mothers called WIC which operates on that premise, and you have to request approval for a substitute product when the items on the approved list are out of stock. But some people are of the opinion that you should be able to buy yourself a steak, or yes a lobster tail, or buy a child a birthday cake because have a fucking heart. (I'm not accusing you of anything, only finishing my sentence for effect. Pax.)