So even if these PUI go for free, who would bother?

Handles (someone convinced me that this is the going word for what I called PUIs) do not compete with names. Think of them as portable IP numbers. They are for all of those applications that require continuity and mobility, but cannot afford to acquire and defend a domain name for that purpose. If a system of handles succeeds widely, then many name services (of all sorts, not just domain names) will choose to map to handles, instead of to IP numbers (since they are more portable than IP numbers) or to domain names (since they are more permanent and less attractive to attack than domain names).

Anyway: Any ideas to replace the DNS in any or all of its functions, should address the question: What will I then put on my trucks, if not www.ourbiz.com?

Handles do not replace the DNS. They provide an alternative to domain names for those who need handles, but do not need names, or wish to acquire names separately from acquiring handles. In the long run, they will make the use of names and addresses more efficient, by providing a technically useful intermediate level.

As long as you can pay for registration of ourbiz.com, and defend it from attack by other claimants, you should do so, and continue to paint it on your truck. A handle would represent the business (within technical network operations, not to the public), independently of its name. It would be transferable to theirbiz, a different company with a different name that bought up the operation. It would be preservable by your company if you changed its name from ourbiz to ourbuzz.

A potential side-effect of a good handle system on the market, is that domain names then compete directly with other sorts of names. Currently, domain names serve as imperfect handles, and also as names. When more perfect handles are available at less expense and less trouble, and when software and the market absorb that fact, domain names will probably be acquired solely for their value as names, and no longer for their value as imperfect handles. I hope that such a change in the market will bring down the cost of domain names, and eventually provide a more efficient and rational market.

To repeat, my proposal does not include the abolition of DNS. It involves offering an alternative, at lower cost, for applications that require handles, and that in the past have either used domain names as approximations to handles, or which haven't been implemented because the owners could not afford to acquire and defend a domain name.