This structure allows every peer to be their own ISP and therefore it's free and secure.
If you have a mesh network with no corporate sites hosted there, then you can't access those websites at all. ISPs group together in these formations called Internet Exchange Points which peers internet traffic through underground lines to another ISP, to access the sites hosted on that ISP. So the way you access internet today is already decentralized as long as the sites you access are hosted on different ISPs from your current ISP.
Mesh are connected to internet via NAT. [MESH] -> [VPN/Gateway] -> NAT -> [Internet]