Closed-form solution makes verification much easier. There's the design and solution space for an engineering system, and then there's V&V.

Yes, you can just ship it and test it in your customer's environment, but that doesn't scale very well if you have to run 1-2 months of testing every time you deploy to make sure the ML model doesn't give you random bullshit that flings the arm around and wack someone in the head or damage other equipment.

Not to mention, IK is something so well understood that it would be stupid not to use it at least as a start to building an arm motion software. It's also much faster than doing inference on a model.