In a free world, you should expect to see different networks, like a network that works with text only (as the internet once was), or a network that has central place for selling products with strict rules to prevent fooling the customer in any way... whatever it is, I am not arguing for any of this now... I am asking why do we have a single network?
Each internet provider is a network, each LAN is it's own network (Local area NETWORK)
For the case your e-commerce network it would cost just about as much to connect every point on the edge to that network as it does to connect to the one we have. If there were ten networks it would cost ten times as much to connect. A lot of people already think internet service is expensive.
If you wanted to have some vetted space where commerce was done at a higher level you could find some way to do that on top of the network we already have.
There are often interconnects between some of them, and some of them do go over the public internet part of the time, but there are also parts of them that aren't accessible from the public internet.
"The" internet is a network of networks – by definition, it is the inter-network net that connects a bunch of other networks together into one interconnected mass. We have it that way because it's useful. Before the internet was popular, having small private networks that you'd connect to over the phone or T1 was common, but people naturally found it useful to be able to connect to others all around the world.
The second half of your question is more talking about applications (or protocols, if you prefer) over that network than the network itself. It's like how our roads and networks are structured... there's an interstate network of highways that connects different cities and states together, but each state can also manage its own smaller highways, and each county or city might have even smaller local roads, and of course some businesses and communities will have their own private roads that the public can't access. But through that shared road network, you can transport everything from passengers to food to goods, on everything from a semi-trucks to bicycles.
Similarly, even if we limit it to just the public internet, it's a collection of a smaller interconnected networks, and different applications and protocols can go over that shared network to do different things:
- Gopher is still around if you want a text-only network, or you can look for the odd surviving Usenet/IRC server.
- Trustworthy ecommerce: Well, that's more a market incentives & regulations question than a network one. There's no magical technology solution to ensure someone won't rip you off. But you can already buy from reputable dealers (i.e. not shady third-party Amazon vendors) and you'll probably be fine.
- There are various semi-private communities that form de facto subnets even though they're transported over the bigger internet, things like every separate blockchain, or Freenet/Hyphanet, TOR sites, or even just Discord, Whatsapp, Slack, Line, etc.
At the end of the day, it's really expensive to drag fiber across the ocean floors or launch satellites, and it would be crazy if every business, organization, and household had to run their own cables. Instead, they can all share that basic infrastructure, but have a lot of freedom as to how they use it (subject to local laws and international agreements, I guess, or else bypassing them with encryption & steganography).