Not true in most countries (including USA). There is a whole service provider industry (WISP) with sizable equipment vendors (Miktotik and Ubiquity) that depends on using the unlicensed bands over wide areas and long range.
Yes, but a) those caps are not so small as to be useless as stated by the parent, and b) there are sub-bands of the 5GHz unlicensed band that allow higher txpower in the US only when deployed "outdoor". This page provides a decent summary: http://www.wisp-router.com/page.php?11
fwiw fear of overwhelming interference from well-funded entities such as carriers is not new. In fact it was very common until the extra capacity in 5GHz was opened up 10 years ago or so. Prior to that you could find a cell carrier in your area decided to backhaul a tower with a T-1 on 2.4GHz, lighting up the entire band with impenetrable noise. Since that time the carriers' backhaul capacity needs increased significantly, driving them to fiber-feed their sites or use 23GHz licensed. At the same time the available channels in 5GHz expanded (through re-use of space previously allocated for military use). So things have been reasonably quiet (sic) on the interference front until this new challenge.
Disclosure: I built and run a very small WISP due to owning a home in a place with no Internet service, in conjunction with making my living writing software (oops!)
There's a big difference in how they use the available power.
WISP-type equipment generally uses very directional antennas so the available power is used more efficiently.
A laptop and a home WiFi router are like people talking in a crowded room. Long-range systems are like talking into a unpowered megaphone while the other side is listening with a megaphone on its ear.
If what the carriers are talking about is highly directional links for backhaul then I don't see what the fear is. Directional is not going to interfere with nearby WiFi.