Then by all means, do.
Although it seems odd that if there were a market demand, such an item would already exist, and there would be no need to twiddle with an established successful product.
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It smells more like a market ploy by the company, IMHO, but if you think well enough of their product to be a Teresa HEINZ Kerry groupie, knock yourself out.
It does exist!
Heinz No Salt Ketchup is in my fridge right now.
This change to the regular recipe makes no sense except
to pander to the Bloombergs of the world.