How many times do people have to spell it out to you Liverpool will get two high speed trains per hour via Crewe and HS2
Okay, so there will be some form of link, fine, though "Via Crewe and HS2" does not sound very "high speed trains" to me, and inevitably there will be even more increased cost to go from the expressway to (eventually) into Liverpool itself.
For much cheaper, much quicker links, just spend a fraction of the cost on upgrading existing track, use South Parkway as an alternative hub rather than trying to get into the city centre.