Here is a quick whirlwind tour of what the your proposed architecture would actually do:
The access layer is responsible for connecting devices to the network. Its defining characteristics generally revolve around either high port density or the ability to overcome physical “last mile” type challenges, like wireless 802.11, or remote access via modems or VPN.
The Distribution layer is where policies are applied. It’s where access-lists, or QoS, and CPU-intensive routing decisions should occur (as opposed to just a default route or default gateway). Distribution layer designs usually focus on aggregating Access devices into boxes with significant processing resources so that policies can be applied.
Finally, the Core is the “backbone.” Its job is simply to move packets from…
I hope this helps in your understanding.