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I don't see why the answer to that question affects whether particles can interact by exchanging particles with each other. To be clear, I'm not taking a stance on whether that's an accurate description of how particles work, but I don't think that it's somehow logically incoherent.

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The point wasn't that particles can interact that way, but that that is how they interact. But that requires infinite regression. (That needn't necessarily be a problem, but it does need a justification.)

We already have mathematical metaphors of such infinity compressed in finite regions. E.g. statistical self-similarity of mandelbrot fractal.

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