There is much more to be learned at school than just what's in the curriculum. Pupils learn how to interact with one another, they learn the importance of authority, obedience, and teamwork, and they learn how to dress smartly. They also learn how decisions are made, and can see the difference between good and bad decision making.
If it wasn't for the requirement to wear a tie at school, I very much doubt I would have learnt how to tie a tie knot competently. If I then started to go to job interviews and carry out office work without the ability to tie a tie, it could have blown quite a dent in my career. But perhaps more importantly, the decision seems to have been made based on completely groundless fears, with no firm evidence to back them up. Children learn more from the example that their parents and teachers set than from what those grown-ups say. So if school authorities don't back up their decisions with clear evidence, and don't consult those whom are affected by the decisions, they are setting a bad example and neglecting their educational duties.
Clip-on ties have their place - I used to be a member of the British Red Cross Society who have insisted on the use of clip-on ties for decades, but that's because when you're treating patients with certain conditions it's not uncommon for them to grab at your tie. But for everyday use in schools, there's simply no justification to insist on the clip-on variety.