It is specifically because you cannot embed a color profile into a quicktime mov using the After Effects output module. Note that Quicktime DOES support embedded profiles, just that most versions of AE do not for that specific container type. (not sure about the newest versions if they ever addressed this).
Notice how the word “embed” is greyed out:

THAT SAID:
Quicktime and in fact most forms of video are broadcast with NO color management. Instead, there are sets of standards such as Rec709, (which defines camera/source gamma) and Rec1886 (which defines display gamma). The idea being that content then plays correctly on devices that are compliant to the standard without the need for conversion profiles or LUTs to be applied.
As for defining your imported video as sRGB – if you always want to import video as sRGB if there is no embedded profile, you can alter the After Effects import preferences in the “Interpretation rules.txt” file:
/Volumes/Boot Drive/Users/User Name/Library/Preferences/Adobe/After Effects/VersionNum/Interpretation Rules.txt
It’s a human readable file and editable with a text editor (keep it plain text, never RTML). It has instructions in the file and is fairly self explanatory.
Andrew Somers
VFX & Title Supervisor
https://GeneralTitles.com