Instead of www.domain.com let's use us.domain.com and eu.domain.com, etc and then break it down by state/province and then city
This would at least allow for several orders of differentiation.... we do it with phone numbers.. ie: prefixes instead of suffixes
This way you could have multiple companies/individuals, etc. as .com or whatever which would still be semantically correct but have them further identified by their region
You could register: us.va.richmond.shoegallery.com for a website/address for a business named Shoe Gallery in Richmond Virginia
Then someone else who had the bright idea of calling their business Shoe Gallery but was located across the country in Oregon could get us.oregon.portland.shoegallery.com
If the brand is a Registered Trademark in your state, you get to have us.oregon.shoegallery.com
If the brand is a Registered Trademark in the US, you get us.shoegallery.com
You could pay to receive a similar license for use in other countries if you had a presence there and did not conflict with an existing brand
The city level domain would be tied to the business address listed for billing purposes
This would allow non-national brands to co-exist in the same country under the same name (which is perfectly legal to do via DBA and business license per city), though you'd still have to respect Trademark laws ie: you couldn't claim us.ohio.bfe.sony.com just because there was no Sony store in your city.
This would also allow businesses to set up local storefronts more effectively, instead of having to ask for your zip code to determine your locality, then redirecting you... all sorts of interesting scenarios come up in fact.
Firstname.Lastname addresses could be organized more effectively.... though they should be .org (to avoid a new tld) not .com ie: us.washington.medina.bill.gates.org
Notice the extra . between first and last... now Melinda can have her own address too.... and any other overshadowed Gates'ians in Medina, WA can have an address as well... though this still could be a problem for the many (Joe Kim)s in the various 'Korea Towns' but it's better odds than they have now.
And that's the whole point right... to give everyone a fair chance to have an address which is unique AND non-trivial
Without belaboring the point, there are better organizational methods than new suffixes... and in fact those should be reserved for functional purposes as they are now... .com should mean a commercial entity, .org should be a non-profit organization (whether a foundation or simply a family group or individual). Use prefixes to add organizational hierarchies... the most effective and least likely to be non-trivial being regional categories.
Using existing Trademark laws to enforce claims, existing franchises can be respected and yet a mom-and-pop can elect to go with an available local domain in the beginning and then escalate their claim as it becomes a regional brand and then a national brand without having to pay up front. The courts would decide who can claim a national Trademark in the event that two regional brands decided to go national at the same time or wanted to instituted their claim in advance against competing brands at the national level... most likely there would be a payoff/settlement and the business who wanted it the most, had the resources to follow through on their claim would get the name, though the business wanting the national brand would have a tough time if they only had one physical address, no matter how big their bank account is.
The biggest issue would be when a business or organization changes physical address.... they would also have to register a new virtual address, if you move out of your city, or your state... though not as big as you might think at first, no bigger than changing phone numbers or physical address really, simply notify interested parties of the new business web address or individual web address as you would for your street address. Certainly not as convenient as being lucky enough to get yourname.com and keep it forever, but who's that lucky anyways? and do they deserve to get all the glory?