Okay so it sounds like my usage is valid if I add the brackets. I will try to come up with a documentation patch as some stage. The reason why it is not supported without brackets is to maintain a bit of consistency with the question mark (?), which modifies the preceding quantifier, and with the plus sign (+), which is also a modifier in other implementations.

For the record, Gnu grep does seem to accept my expression (although Posix says this is undefined, and neither support lazy or possessive quantifiers):

$ grep -E -o 'a{2}*' <<< "aaaaa"
aaaa

However pcregrep, which supports lazy (?) and possessive (+) quantifiers, doesn’t like my expression:

$ pcregrep -o 'a{2}*' <<< "aaaaa"
pcregrep: Error in command-line regex at offset 4: nothing to repeat
[Exit 2]
$ pcregrep -o '(?:a{2})*' <<< "aaaaa"
aaaa