The New Deal ultimately was a band-aid to prevent a violent revolution from taking place, a desperate plea from Roosevelt to the rich to ease off before the top blows (and even then, the rich were pissed off enough by that to try for a coup attempt).
WWII and strong unions caused those changes to stick for a time, but the problem is history has shown us that with capitalism, it's only ever temporary relief. Eventually the rich simply can't take it anymore, and they plot against the common man with renewed vigor. They finally got the ball rolling for their benefit in the 70's, and its been a steady decline since then, as they spread doubt, bust unions, bribe politicians who are all too willing to help for a pitiful amount of money or a free camper. Then when the rock is almost entirely milked, as it is now, and as it was back in the gilded age, instead of letting up, they squeeze harder.
You would prefer another New Deal, another breather for the working class where the rich capitulate and give up a slightly smaller piece of the pie again, and let us live a little better for a few more decades.
Problem is, the world wasn't on the brink of climate collapse in the 1930's. A repeat of that solution, for capitalism to be reigned in, but still relying on infinite growth to survive, simply isn't compatible with a livable biosphere for 10 billion people. If we try another New Deal reset, we'll simply make the lives of the working class in first world countries a little easier while the equator burns, and the poor die en-masse as they migrate and struggle for water.
Authoritarian communism certainly isn't the answer, history has proven that time and time again. But if we're to survive, capitalism must end soon, that much is assured.
Anarchism has shown the most promise in history before being quashed by the authoritarians. The rich and powerful will fight it violently, but if enough people come together and resist through merely withholding our labor, we could implement it mostly peacefully, and once that genie is out of the bottle, I very much doubt most people would prefer to go back to capitalism (I'd highly recommend reading The Dispossessed by Ursula LeGuin, to get an idea of what that sort of future could look like).
Whether or not markets in some form exist is another matter, and one that would need to be experimented with, but basic essentials to life should be free to anyone. Markets could exist for non-essentials.
No one would take your potatoes. Anything you grow or build by yourself is your own personal property that is yours to do with as you wish.
The grand idea of an Anarchist society is that if we collectively worked toward just meeting everyone's basic needs, it would remove the ability for people to coerce others to work for them under threat of homelessness or starvation otherwise (our current arrangement in society).
This basic work to meet the essential needs of everyone, if mostly automated with the aid of machinery and computers, would realistically mean everyone would collectively only need to pitch in about 3 months of their time per year to maintain a reasonable standard of living, the rest of the year would be free time to do with as they please, to form cooperatives with people on equal footing, to spend time with family, to garden, or to create art.
This collective work could not be enforced with violence, coercion, or a state (as none would exist, ideally), otherwise it would quickly descend into authoritarianism. It would have to be taken up willingly by individual communities, and it is very likely they would do so once the benefits are made clear and they are not under the yolk of capitalism coercing them to worry about themselves above all, and instead begin to think on a collective as well as an individual scale. It would be a stark improvement in quality of life of 95% of the population, something unseen in history except briefly during the Spanish Revolution.