Who says you need “last mile stuff”. Go satellite/wireless.
And there's no reason you can't build your own 3-stage rocket capable of lifting 10,000 pounds of payload either. Go ahead, try it. Do you plan to use materials commonly found around the house, or are you rich enough to finance the internetworking infrastructure with commercial/industrial quality gear? Do you have even an order-of-magnitude approximate idea of what such a system costs, not only in equipment, but in paid employees to maintain it?
Then there's that little annoying item of how you connect to the existing internet. Because you're going to have to do that, or else your alternative net falls apart. You HAVE to acknowledge and work with the existing internet, period. So whatever protocols you devise for your network, they will have to be compatible in some fashion with the established standards, or else you'll be isolated and no one will come to play with you.
> Who says you need “last mile stuff”. Go satellite/wireless.
Ummm, in that case your satellite/wireless link -IS- the "last mile". Sooner or later, you have to get to the end-user's computer, or mobile device, and that's what's called the "last mile", whether literal or figurative.
Look, I'm not saying it's impossible to build a network, hell I'm a Network Systems Admin -- it's my profession to build and maintain networks.
What I'm saying is that it's wildly impractical and expensive to try to build something like the internet, or even a tiny piece of it. I'm saying that any alternative internetwork system would never in fact support communications beyond chatter, which is more easily done with radio and similar non-packet technologies. If you really want to shoot for a packet-switched network, that's also an established technology over radio, and has been done for decades.
But hey, if you think you can build an alternative network, can employ the trained professional personnel necessary to maintain it, and develop the wide usage and high reliability that can attract serious support from the businesses and banks who will make your network functional, you go right ahead, and God Bless you.
Hell, you succeed at that, and I'll come work for you. :)