There are 4 kinds of devices, I believe, that make any sense for the FCC to care about:
1. Passive antennas
2. Radios intended to transmit (which do not include an antenna)
3. Radios intended to transmit (which include an antenna)
4. Electronic devices not intended to transmit but that, nonetheless, do radiate (EMI)
Passive antennas are the only category where what you said makes sense. But I think all the FCC cares about passive antennas is what the FAA cares about passive antennas: that they aren't so tall as to knock an airplane out of the sky. An antenna receives as well (that is, with equal gain) as it transmits, so characterizing their gain is important when matching an antenna to device type (2). Typically the FCC wants to approve the entire system (devices in the third category), because it is virtually impossible to know the consequences (including increases in EMI and harmonics that suddenly pop up) of attaching, for example, a 6 dBi antenna to a 100 mW 2.4 GHz WiFi card. But the FCC also must approve the radio (category 2 above) if it is sold separately and then put together by somebody else. A radio will get an advisory that it should only be coupled with antennas equal to or below a certain gain.
Otherwise, a radio in receive mode essentially falls into category (4), which, in other words, needs to pass the same requirements as the computer sitting on your desk does. But the FCC doesn't care if you put a 60 dBi antenna, sensitive to a restricted band, with a receive-only radio.
The PURPOSE of the FCC regs is to keep people playing well together. And it isn't like you listening on a frequency causes somebody else to NOT be able to listen in on that frequency.