I really don't think that ARPA (as it was then) was spec'ing a worldwide commercial network.
It's research was in self-healing communication networks useful for military communications where many parts of the 'net might be taken out. This would be (and is) used on closed encrypted networks with no public access.
Also, don't tar the original research into packet switching with the poor implementation that plagues many applications now on the Internet.
Of course, there were weaknesses in the original design, such as the DoS SYN attacks or man-in-the-middle data capture attacks that are possible, but the security layers that leak so badly are definitly above the one provided by the basic ARPA design.
If you look at the original suite of applications that were demonstrations of the work (telnet, tenex, ftp, mail), they were useful, and people used them, even if they were basically insecure. The world was a more simple place, and generally the networks they were used on were internal to single organisations. Even then, firewalls were mooted (the first firewall I was aware of pre-dated the Web. by several years).
The concept of the World Wide Web (which is just a service running on the Internet) was NOT part of the ARPA research.
The fact that we are still using it, warts and all, justifies the strength of its original design, and it is only likely to be replaced by a derrivitive work (IPv6).