Landlords would lose income left and right.
The relevant question is: would society stop the building of these free houses to protect the interest of the landlords?
(Now, take that analogy and throw it in the trash. ;) Housing is essential; art is fundamentally a luxury good. If we want to, we can have a society that protects profit-making on luxury goods and profit-making on necessities differently. "Someone is losing income, therefore this change is bad" is too simple a rule to build a healthy society upon, but a reasonable person can conclude "Artists are losing their livelihoods, therefore this change is bad").
Money is just paper. And now with cashless systems, it's now only bits on some computers. But no one sane wants to maximize everyone accounts or print cash to hand out. Art takes hours, days, even years or human labor to produce. Copyright laws set an artificial scarcity, because if it can be replicated at no cost, there's no way for the author to recoup the cost of production.
In the analogy you provided, you'd still have to deal with land scarcity and environmental impact.
Well, depending on whether one considers the output of one of the AI image diffusion algorithms "art"... Not anymore, right? That's rather the point of the debate? That we've gone over a few decades from a world of "This wall is blank. Maybe I'll go to the art show and find a piece someone made, or commission a piece based on an idea in my head" to "This wall is blank. Maybe I'll spend two hours futzing with DALL-E and send the result off to a local print-shop, then pop it over to Michael's and frame it?"
But they are free to use the fruits of the model, same as anyone else. I suppose the difference is they don't care; they already have the talent to transform their labor into visual art, so what use do they have for a visual-art-generation machine?
I find strong parallels in the building of web crawlers and search indexers, except... Perhaps the indexers provided more universal, symmetrical value. It's hard to make the case that someone crawled and added to a search index doesn't derive value from that strong, healthy index being searchable (even librarians and news reporters thrive on having data indexed and reachable; the index is a force-multiplier, it's not "stealing their labor" by crawling their sub-indexing work and agglomerating it into a bigger index, nor is it cheapening the value of their information-sorting-and-sifting skills when the machine sorts and sifts).
So perhaps there is a dimension of symmetry here where the give-and-take aspect of what is created breaks. Much like the rich don't have to care whether it's legal to sleep under a bridge, artists don't have to care whether a machine can do 60% of the work of getting to a reasonable visual representation of an idea. No, more than that: it's harmful to them if it's legal to sleep under the bridge.
They'd be landlords in this analogy, crying to the city that because people can sleep under bridges the value of the houses they maintain has dropped.