There are two simple reasons why I like microfoundations:
1. Because the economy is what people do. Understanding and explaining economies is understanding and explaining why people do what they do.
I don't care how well your VAR fits the data, and how well it keeps working across lots of different policy regimes; it's still not an explanation of why people do what they do. It is not an economic explanation. It is instead just another interesting fact about the economy that needs to be explained. Why do people do those things that make your VAR fit the data?
Let me give you two recent examples where I became upset because of lack of microfoundations:
The standard New Keynesian model does not explain why people should expect other people should choose to spend enough to ensure the economy converges towards [the natural rate of] full-employment. It just assumes it, without explaining why. I want to know why people expect other people will choose to do this.
The recent kerfuffles about higher nominal interest rates causing higher inflation. I want to know why higher nominal interest rates would cause people to choose to increase prices more quickly. I got no explanation why.
Those are two very paradoxical examples, because they come from supposedly microfounded models, not VARs. Which is why I got upset. VARs don't even pretend to explain why people do things. I don't get upset at VARs. They are only VARs. I don't expect anything better from them.
2. Because good policy means doing what people want. There are only two questions that matter for policy: Is this macro model like Prisoner's Dilemma? If so, in what ways, if any, could we change the game so it isn't like Prisoner's Dilemma? (Or maybe: Is this macro model like Stag Hunt? And if so, how could we flip it to the "hunt stag" equilibrium?). You can't ask those questions if you don't have people in the model.
We don't care about GDP, for example. We could increase GDP by forcing all the old people out of retirement and making them work. But that maybe isn't what people want. If your model doesn't have people, who want things, we can't tell if a policy change would be good. Unless we don't care about what people want.
We can invent all sorts of reasons about the practical usefulness of microfoundations. But when it comes right down to it, none of them really matter to me. I want microfoundations for their own sake. I want people in the model. I want the model to explain to me why people do what they do, and if a policy change would be good for the people in the model, by helping them get what they want. Incredibly stylised one-dimensional people are much better than none at all.