We could simply check it into the site-packages inside the CPython source 
tree could we not? *Not* providing a bootstrap script and merely checking it 
into the default site-packages means it's available for everyone. No matter 
how python installed. If Linux packagers really don't want it installed by 
default they could simply just remove it and either install it along with 
Python, or continue to keep it how it is today as a separate package?

This sounds an unnecessary complication.  I suspect that there is a 
small minority of users who actually build Python from source.  And they 
should know what they are doing.  I believe most users either use a 
distribution-provided Python (via their OS) or a third-party package 
provider (including python.org binary installers and their derivatives).  
The OS distributors are going to do what they currently do; the only 
change needed is to persuade them to include their pip package as a 
mandatory dependency.  Trying to hack the Python source build process to 
include a copy of pip is just not worth the effort.