Wouldn't a wider width give it more throughput?
Theoretically. The problem with the 2.4 GHz range is that it's SO limited as for spectrum as compared to 5 GHz. By having a 40 MHz width plopped effectively around channel 6 your wireless signal reaches into and is impacted by ALL other 2.4 GHz wireless traffic.
Here's an example below. Usually with 20 MHz width you have 3 separate non-overlapping channels. If you had your 40 MHz channel at either end you'd still be impacting the below (but, as yours is in the middle, it hits every other neighboring wireless traffic on the 2.4 GHz ISM band).
Correct me if I'm wrong, but doesn't just running 802.11n and eliminating all over wireless modes share a faster speeds for clients connected on a subnet?
Not necessarily. Enabling N just adds another set of 'high speed' rates. The other rates are still available and negotiable between clients. It would be a very bad idea to completely limit other data rates as the client will negotiate a slower data rate in response to a weaker signal that may not support the higher rate. The router may simply designate a client as N if it advertises it supports rates higher than 54 mbps.