I get what you're saying but I don't think that's the right analogy here.
Part of the cost is the amortization of the development cost of building and training the model. Perhaps that's why there is a monthly subscription component. That would make economic sense, although I suspect it's more psychological in that you want people to use your product and a subscription makes that easier. If you think about the cost of each generation then you're not going to have a good time using it.
My point was more though that you pay for the convenience and the inference cost. I can also make my own bread, but my local bakery or supermarket can make it much more efficiently at scale and cheaper.
Then you are arguing a point no one tried to make. They didn't say "Why do I have to pay for those people's work?"
It sounds like a valid argument that you did not articulate was "You can buy a house, but if a house costs way too much to buy, then another option is you can rent it." The house is a fixed static good like a local piece of software, but it just costs so much in total that you can't afford to buy it and have to rent access to borrow it. You can't copy a house for free so it's still not quite there but the essense is.
So maybe the model costs so much to create that if you were to buy it, it would have to cost ... Well the Chinese say they made a model for $6M. So that could be as little as $1 per person if it goes popular. Let's make it $100 just to be over the top generous. So maybe the analogy and the excuse for the subscription still doesn't wash.