Coase: βOr, alternatively, if this operator had the right to cause interference, he would be willing to desist if he were paid more than the costs of suppressing the interference or the decrease in the value of the service he could provide if interference were barred. And the operator whose signals were interfered with would be willing to pay to stop this interference an amount up to the decrease in the value of his service which it causes or the costs he has to incur to offset the interference.β
Why would the operator have to pay to stop this interference if he owns that spectrum? If I go onto your land do you have to pay me to get me off of it? No, you have legal protection protecting that property right against non-consensual trespass.
Similarly, we can then conclude the operator must not have a property right of that spectrum if he must pay to prevent trespass, otherwise the operator would be able to file a criminal injunction to prevent the interfering individual from continuing to disrupt his signal at little cost--as you would do for a land trespass.
You're confusing the specific bill he mentions in the preceding section about the legal etiology of the FCC, which had proposed to do exactly what you're mistaking as the argument of Coase; where Coase thinks only that that specific bill shouldn't have been dismissed so trivially and as a resolve to the current situation where the FCC has already sold partial licenses--but leaves it thoroughly short of an advocation as he develops the case of no special regulation for broadcasting rights.
In the Chicago School monopolies are impossible; or rather, monopoly pricing is a fiction.
I can't find a direct top-down subdivision quote (my copy isn't searchable; he might not literally say it at all[1]), but efficiency of the single initial auction winner scenario can be logically inferred from what he explicitly says. For example, on pp 20-21 he says that in a property regime broadcasters would be able to assemble larger bands through free market purchases, subject only to their ability and desire to pay. Efficient aggregation and subdivision of spectrum is a built-in presumption.
AFAIU, applying Chicago School principles, the price at which a single owner of all spectrum would subdivide and sell a portion would have no (or at least de minimis) monopoly profit component. Another way to look at it is that ownership of any contiguous range of spectrum, just as with a contiguous piece of land, is by definition monopoly ownership. Breaking contiguousness might require a premium, but only proportional to the economic value from contiguous usage. Breaking contiguousness of all spectrum would require a premium proportional to the marginal additional usage value, which for all spectrum is pretty much nil. What usage of all spectrum has a value greater than the aggregated value of using two, smaller portions? More likely there's greater value in the latter than the former. At some point subdividing becomes inefficient, but certainly at that point we're no longer dealing with a single, contiguous band of spectrum. The initial, profit-maximizing owner has already subdivided most it, and probably no longer owns any of it--our hypothetical bid winner was probably a specialized broker banking on extracting value by subdividing it.
Of course, judging by your comment, we both believe that monopoly profits are real. Minimally they're approximately equal to the transaction costs required to buyout or break the monopoly, which is approximately equal to the cooperation costs for victimized buyers, which in practice would be born by a prospecting broker. (What we intuitively think of as "monopoly profit" are the opportunity costs to buyers having to pay a premium over the price paid in a competitive market. But we don't include those costs in the buyout/breakout scenario because they're recovered after the fact in the hypothetical and cancel out.) AFAIU, according to the Chicago School these transaction costs are de minimis, especially with large, liquid financial markets. This is why they're such fans of financial market deregulation, derivatives markets, short sellers, private equity, etc. But many people, including some Chicago School luminaries after 2008 (e.g. Greenspan), aren't so sanguine about those costs.
And this explains why AT&T and Verizon don't behave like the efficient economic actors in Coase's world--they won't subdivide or sublease their spectrum down to the levels required for WiFi-like usages because the costs of all of us cooperating to collectively bid is too high. Actually, that's not strictly true--the costs of cooperating can be trivial if we move beyond simple market theory. All we need to do is democratically choose, directly or indirectly, for the FCC to expand unlicensed spectrum, marginally rolling back a regime we previously democratically created.
Yes, I get that Coase in particular was appreciative of transaction costs in other contexts, such as in the theory of the firm. But Coase, and people in general, often make implicit assumptions about relative quantitive costs that become assumptions about qualitative costs that in turn become judgments about whether transaction costs are substantive. The transactional costs of subdividing and transferring spectrum among TV, radio, military, and other large, traditional broadcasters undoubtedly looked de minims in 1959. Certainly they were lower than the costs of FCC central planning, and that much I can't disagree with. But 40 years later the environment had completely changed.
[1] I distinctly remember seeing illustrations of this arguing-to-the-extreme concept, but the illustration itself was probably from another author as a gloss on Coase's work.