Do you think the people who designed HS2 have not considered these aspects?
You analysis is very narrow and only considered the benefits to a certain set of people.
HS2 actually follows reasonably closely to the old GCML. And for the same reason, its the best route to build a fast rail-line along.
I think your proposal complete ignores the additional cost of such a route change. And the cost alone, aside from anything else would make it unreasonable.
Many things go into selecting a route and in most cases where I think they made the wrong choice its usually because of cost concerns, like not building the needed tunnels into cities.
I actually don't think that's true.
The reason HS2 route cost so much money is because so much is tunneled. Why is so much tunnelled? Because rich people live there and won't accept a blot on the landscape, partially because they don't see a personal benefit.
If you can remove the tunnels it doesn't really matter that the route is slightly longer or has slowly less optimal geometry.
That not totally true. Yes, HS2 spend additional billions on tunneling. But even without that you don't magically solve all the issues and in some places where they do tunneling its actually not completely stupid. Tunneling accounts for a few billions, not many 10s of billions.
And you don't get magically rid of all issues with people complaining, because guess what, other people live on that other imaginary route that lives in your head, and they would demand tunnels too.
And its really the politicians fault, a few people who don't like the look of the train should not have the power to stop it, specially not in a place as centralized as England.