Each read in a fastq file makes up 4 consecutive lines (read id, read sequence, qual id and qual string). What do you need the qual id for? Isn't the read id enough for identification? Besides, in most fastq files (if not all?) the qual id is just "+"
As described in this paper:
The FASTQ format was invented at the turn of the century at the Wellcome Trust Sanger Institute by Jim Mullikin, gradually disseminated, but never formally documented (Antony V. Cox, Sanger Institute, personal communication 2009).
so we can't be all that surprised that the format has some unspecified characteristics.
this prompted me to look up more information on Jim Mullikin, turns out he is a Director at NIH Intramural Sequencing Center
I think it's there to serve as a delimiter. One of the most common issues we have to deal with is the problem of line endings caused by going from different operating systems. When Fasta files get messed up because of this you can at least tell where the sequence ends because the header starts with the greater-than sign. It would be chaotic if not for that delimiter. Likewise, I think it would be more difficult trying to find where the sequence ended and the quality line started without this '+' delimiter.