That is part of the problem, yes. Not SNAP itself, which is good, but the fact that it can be used to buy garbage.
You should be restricted from buying soft drinks, chips, candy, etc. with SNAP/EBT, just like you can't buy cigarettes and alcohol with it. But nobody is willing to take on BigFood, and are content to let them prey on the poor with taxpayers footing the bill.
The second problem though is that if you restrict SNAP eligible food, you still have to provide healthy alternatives -- fresh veggies, fruit, grains, etc. -- at subsidized prices for SNAP recipients so they can actually survive on it.
It's such a shameful situation, and one that gets very little attention from either party.
As the great Charlie M used to say: "Show me the incentives and I'll show you the outcome"
but we can't change it because that means we are making poor people miserable