Hey, some of my best friends are from Saitama!
I think the answer to why the various Shinkansen are not connected boils down to this:
1. The tracks aren't currently connected, and it would cost an not-insignificant amount of money to connect them (a cost borne by whom?)
2. There are many more passengers boarding and disembarking at Tokyo than passengers who are traveling through Tokyo to make the cost of #1 worthwhile
3. By having connected operations, schedules become much more complex and susceptible to delays during IRROPS due to the tree-like structure of lines running through JR East territory
4. As companies JR East and JR Central are not necessarily on the same page when it comes to this issue
Technically, while possible, connecting the systems would require a level of logistical planning and (corporate) political will that just isn't there right now. I would much prefer the government and/or the JR companies spent their money on better connections to HND from points beyond Tokyo or longer train lengths and platforms on the Chuo Line to reduce overcrowding there.