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Actually, believe it or not, for many years not it has been the case that you do not need a radio operator's license to operate an aircraft radio unless you plan on flying internationally. Anyone can order a handheld aircraft radio from Sporty's. On the other hand, you are still obligated to follow the regs. There seems to have been little or no problem with the license-less situation, though homeland security types can surely dream up scenarios...

Actually, believe it or not, for many years not it has been the case that you do not need a radio operator's license to operate an aircraft radio

THAT may be what it seems like - but there are regulations that cover even that (when was the last time you were required to obtain a operator's license to use a cell phone?) ...

Aircraft Radio Stations
The Telecommunications Act of 1996, which became law on February 8, 1996, brought about fundamental changes in the licensing of aircraft radio stations. Aircraft radio stations include all types of radio transmitting equipment used aboard an aircraft, e.g., two-way radiotelephones, radar, radionavigation equipment, and emergency locator transmitters (ELTs). The primary purpose of aircraft radio equipment is to ensure safety of aircraft in flight. This page provides a summary of the recent rule changes and gives guidance to commercial, as well as general aviation aircraft owners, concerning the licensing and operation of aircraft radio stations.
 Who Needs an Aircraft Station License?
 How do I get a License?
 General Information
 FCC Information (Forms, Fees, Rules)
Who Needs an Aircraft Station License? On October 26, 1996, the FCC released a Report and Order in WT Docket No. 96-82, FCC 96-421 (text, WordPerfect), eliminating the individual licensing requirement for all aircraft operating domestically. This means that you do not need a license to operate a two-way VHF radio, radar, or ELT aboard aircraft operating domestically. All other aircraft radio stations must be licensed by the FCC either individually or by fleet.
WHICH AIRCRAFT ARE INCLUDED? The new rule applies to all aircraft, including scheduled air carriers, air taxis, as well as general aviation aircraft, so long as they fly domestically.
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MAY I USE MY HAND-HELD AIRCRAFT VHF RADIO ON LAND?
You may only use your hand-held aircraft VHF radio from your aircraft, or under the authority of an FCC ground station authorization. Ground station authorizations are usually only issued to aviation service organizations located on airports, businesses engaged in pilot training, aircraft manufacturers, or persons engaged in chase-car activities related to soaring and ballooning.

More:

http://wireless.fcc.gov/aviation/fctsht4.html