OK, I buy that. Instead of focusing on demand, govt could look at the supply side.
Let's be generous and assume lower wages is not the solution. I doubt the goal here is cheaper food at the cost of misery to others.
So there's rent as the obvious contender. In some parts of the country rent is high because supply is low. In NY there's not much one can do about supply, but in say SF property supply is very much under govt control. So loosening up zoning there, and allowing for more development would be a step. Of course there are a lot of people invested in that not happening - specifically landlords - which means the govt has to pick winners and losers (or more accurately choose different winners, since they are already choosing winners and losers.)
Now granted the original poster was clearly talking in the context of restaurant food prices, not actual "food prices" - but its worth noting that zoning changes wouldn't affect general food prices, and the impact on restaurant rents would be long term, not short term.
The other big input cost, direct and indirect, is energy. Fuel for cooking, and perhaps more significantly for transport.
I'm not sure the govt can do a whole lot there - yes there are taxes in there, but they are low compared to global standards, and reducing them just means making them up elsewhere. (which might not be a bad thing, but tax policy moves very slowly.)
The price of oil is not really in govt hands, pricing there is international and very fluid. Unlike most oil-producing countries, the US does not determine local supply.
So we're back to labour? But even there labour isn't over controlled by govt. Min wage is already pretty low, and given the high employment rate labourers can afford to hold out for higher pay. Its not like people working is restaurants are rich, even most owners barely break even, so again this doesn't look like an area where govt could do much - except encourage poor immigrants maybe? (in the UK low-end posts are getting hard to fill since brexit)
And I'm not sure lower restaurant prices at the cost of human misery is really the goal here.
So, in summary, what other govt options are in play? Zoning would have an effect in some locations. Is there anything else that would have an impact? Especially in a short time scale?