> That alone doesn't guarantee that those theories would fit future data.
Sure, but that's sort of a triviality. It's true for any theory.
> It's a two-way process. You need experiments to improve theory, and you need theory to create experiments.
I agree that it's a two-way process but I wouldn't say you need theory to create experiments and I think I've given sufficiently many counter examples to illustrate this.
What we (as humans) do need theory for is to make sense of our experiments (or of the world, really) and discover new experimental setups that might uncover something interesting (not explained by the current theory). On the other hand, without theory there's no concept of "unexplained by theory" in the first place. Our experiments would probably resemble random walks (in the sense that they're not driven by theory) but that doesn't mean we couldn't uncover interesting phenomena, let alone run experiments at all.
Getting back to the "making sense of the world" point: Take an AI for instance. It could probably be trained on experimental data alone and make suggestions for future experiments and give predictions, without a simple, coherent and human-understandable theory behind them[0]. This, too, illustrates that experiments would be possible (and worthwhile) even without theory.
Note that I'm not at all trying to play down the role of theory. To the contrary, I'm saying all this as a former theoretical physicist myself. I just see experiment and theory as equals.
[0]: Isn't this more or less what a human baby does as it learns?