UK Rail and Trains

A "rival operator" in the sense of route duplication seems utterly pointless. Assuming finite capacity and demand for tunnel crossings, that'll mean halving the customers for each operator carries, reducing opportunity for economies of scale, increasing complexity for ticketing etc. Unless there's some suggestion that Eurostar is price gouging (and they're hardly wildly profitable compared to other operators) it won't do much.

What we do need is more diverse routes with different destinations (so that not everything is a transfer at Paris or Brussels). There probably is capacity for that, but Eurostar (and other operators who have dipped their toes in) have generally concluded that the demand isn't there to make the routes sustainable (at any price).