I think it makes sense if you think about it.
If you were allowed to cancel short notice, people could book up really prime periods of leave (like you have) as a sort of holding position to see how they felt later on. And then cancel without losing anything.
Thats really unfair as it basically means you’re putting back the time when you need to decide on that leave at the expense of others.
Holding on to prime periods of leave means that others like your colleague can’t book them, and as you’ve seen, missed out on the chance to go on holiday at a reasonable price.
You’ve correctly identified why this period of time was so valuable - you get ten days off at the cost of only four days leave.
You’ve still got that nice break from work, so enjoy it!
The other reason for not allowing people to cancel is that employers want people to take leave evenly throughout the year rather than all trying to get it at the end of the year, or wanting to carry it over. Then it builds up and you have people off for unworkably long periods, possibly at the same time.