It is a difficult twisty poorly signposted walk even though quite short, certainly not good 'space syntax' as the architects would refer to. Any route via Underground takes just as long with long underground passageways, escalators etc to reach platforms but at least you don't get wet if its raining. What's really needed is a significantly improved covered pedestrian route equipped with travelators. The distance isn't any greater than many inter-terminal or terminal to gate links in airports. See my suggested design here -
http://www.townend.me/files/kxlink.pdf
That's certainly a better than the existing solution of walking along the half a mile route between each station entrance (which could be quite a bit longer as an end to end walk if switching between two 400m services at each station). But it does highlight one of my biggest issues with HS2 as things stand, and that's this issue of distances between existing infrastructure & the proposed HS network at a number of points. There seems to be a kind of "It gets you close" approach to interchanging between services, but at places like Leeds, Birmingham, and between HS1 & HS2 if the link is dropped transferring between networks could get problematic. The argument for the accepting the distances seems to be that this is what happens at airports so people will accept it, but generally speaking if you travel by air you allow considerably longer connection times between flights (usually hours) than you would between trains (usually a handful of minutes).
But the truth is that this can be off putting for many people, as the architects might consider the transfers as been "seamless" but the application is often very different. It's not just the distance, it's the number of bodies in front of you, the speed of escalators or travelators, its how many station / G4 staff you have to display tickets to on your route etc. Try transferring from the front of platform 13 across the station to platform 1 at Manchester Pic in a hurry at peak times & you'll know what I mean. I would much rather that existing lines were to share the same terminal that the HS ones would, as ironically they will at Manchester. I understand that this would potentially add to the cost, but building an effective HS network isn't just about doing it for the least cost possible. It has to work for the people using it, and all types of people using it. The current set up is probably OK for commuter traffic, but I wonder what it would be like carting a family with suitcases from the standard lines at Leeds onto HS2, through London & onto HS1 would be like? I can imagine a fair bit of stress & shouting going on.
I do doubt that better connectivity will be built in, as there is now an obvious push to get things moving. I just think it would be nice to think of the networks future users for once.