Insight arises as a simple starting point is chosen, and complexity is gradually built on top of it, as observed physical features remain unaccounted for. This type of insight, of understanding, cannot be afforded by any first-principle calculation, no matter how accurate

I think the above is mostly true, specially when “emergent phenomena” are involved. I would say, though, that first-principle calculations can provide, at the very least, some insight into what ingredients you put in your model. Knowing, e.g., an accurate band structure for, say, a class of materials/molecule/tunnel junction/etc., can help one to formulate a better, more consistent, microscopic “toy model” for these systems.

I guess the message is that we “toy modelers” can always invite our DFT friends
over to play … and have some good theoretical physics done in the process!

(And also, a more complex model is not automatically “better”.)