Sadly I have it on good authority that the reason that the ATSIN was issued because of a couple of rather unfortunate incidents when controllers tried to stop an aircraft at high speed - and for wholly unnecessary reasons.
"Good authorities" are very good at making judgements after the fact from the comfort zone!
I'm familiar with one of the incidents which lead to the above ATSIN being issued. A trainee had sent an aircraft around (quite correctly) from about 1.5 miles and decided to stop the aircraft which had been cleared for take-off. The aircraft was NOT at a particularly high speed and was stopped with over half of the runway distance remaining. Part of the problem was the visual perspective from the tower which meant it was difficult to judge the aircraft's speed, and part of the problem was the perception of the trainee that stopping the departure provided an extra safety barrier, which was not the case in this example because the go around was already turning away from the departure before reaching the threshold. The ATSIN was correctly issued to raise awareness of the issue, and very deliberately does not try to proscribe stopping a departure. There are circumstances when a go-around is unable to make a turn immediately (weather springs to mind, but others can also occur) and then stopping an aircraft already rolling may be the best option. We should all be aware that stopping a departure is fraught with problems, and the ATSIN was issued for that reason, and that alone.
Don't believe everything you're told!