Well, in Nome, Alaska a single can of soda is $1.69.  A gallon of milk is $5.79.  So that's about ten cans of soda in a gallon, so $16.90 for a gallon of soda.  But to be fair, the "cheaper, healthier alternative" to soda isn't milk. Its water.  And that's pretty much free and comes out of the tap.

Soda purchased by SNAP recipients, is done for the same reason that anyone else buys it, it triggers the pleasure sensor (dopamine) in your brain.  Something that water doesn't do.  They're not buying it because its a cheaper alternative.  

Soda, sugar, snacks; they're pleasurable and addictive.  And we're paying people to decrease their health and supporting an entire industry at the same time.  We have every right to decide as a country what we want our government benefits to be spent on.
 
Hence this is a government/societal problem and not an individual consumer problem.