In Australia, we provide lunches for our kids to take to school with them. Most schools have a 'tuckshop' where kids can buy treats (icecream, chips) by paying cash on the spot, or parents can order and pay for meals (typically online) beforehand. But that's usually on occasion as a treat and not a regular, daily, lunch provision.

Wouldn't there also be an associated rise to the cost of living? As the cost of transport rises, food produce etc. will all become more expensive as a result? These costs typically impact the lower-income population more quickly and heavily than the middle and upper income earners.

Just because you prioritize transit in cities, doesn't mean that transport costs in general rise. Transportation between cities can remain car driven as those are inherently sparse areas anyway; you don't need to reduce use of all types of cars in cities, industrial use / deliveries can still exist in those systems anyway; and as a long term idea, self driving deliveries may also drive some of these costs later on. Additionally, while cost of transport rises for car commuters, it very well may fall for transit ones and especially for those car commuters who switch to transit. So it's not a given that prices would uniformly rise.

The cost of driving would rise, but the viability of other modes would also increase, and those other modes are generally much cheaper than driving. Note how Americans spend close to double the share of their income on transportation as the Japanese do: https://www.bls.gov/opub/btn/archive/how-do-us-expenditures-...

If food needs to be more subsidized, then it should be subsidized more directly, rather than with broad transportation subsidies that create perverse incentives for unrelated activities.