A potential limitation of TV "white spaces" arises from the relatively large wavelengths associated with these lower frequencies (lower than mobile or Wi-Fi). At cellular frequencies, and even better at Wi-Fi frequencies, wavelengths are quite short (at 5.8 GHz, a half wavelength is 2.5 cm, i.e. 1 inch), so it becomes relatively easy to build highly directional antennas. Not so with TV frequencies.
Here's a picture from a wonderful article by Neal McLain about highly directional VHF TV antennas in the CATV industry.
[This] antenna was erected in about 1965 [near] Merced, California, [for] a CATV system owned and operated by General Electric Cablevision until 1986. The screen was about 90 feet high and 360 feet long. The radius of the torus was about 100 feet. The screen was centered on San Francisco and several antennas were placed along the locus of feed positions to cover all the Bay Area signals. The support structure consisted of steel towers with the appropriate curvature and the screen was constructed using horizontal, stretched steel wire.
This is an extreme case, but it's worth remembering. Today, semiconductor technology makes it possible to do MIMO and, in the very near future, adaptive beam forming, in silicon at consumer price points. As a result, we're on the verge of major performance gains for wireless, at short wavelengths. That's 2 GHz and 5 GHz, but much less so TV white spaces.
TV white spaces will be useful for applications that must penetrate trees or heavy masonry but, as I commented earlier, the real action over the next 2-5 years (and beyond) will be at frequencies, like 5 GHz, where highly directional antennas can be built in small spaces.