Who's talking about subsidies? The talk is of facilitating competition.
Why would a competitor not go after the same market? If the market will pay the fares, they'll undercut them by just enough but won't be offering Easyjet or Ryanair level prices.
Yes, and more reason to facilitate competition.
Again, there is nothing stopping anybody from applying for access yet nobody has chosen to do so on their own terms. So the only way to facilitate further competition would be to provide direct support to a competitor. Now why would the (any) government pay somebody to compete against Eurostar when there's Ryanair, Easy Jet, BA, etc all competing on price on their own?
It's worth pointing out that it is in HS1's benefit to have additional operators, so it can spread it's overheads over more track access fees, and have increased footfall through it's stations. Although the owners of HS1 Ltd being part owners of Eurostar doesn't help that, but then who made the decision to sell both at the same time? Oh yes, the government (Cameron and Osborne, specifically, sold the UK Government shares in both HS1 and E* to a Canadian Pension Fund).
I'm all for competition, I'd love DB to open a competing London-Cologne route, as they came extremely close to doing, but I am just pointing out it's already freely available, and the reasons it hasn't happened are nothing to do with monopolistic practices by E* but to do with the fundamental economics of the Border situation and long-distance train travel.