I'd agree that as long as the cost of the flights isn't increased by an employee tacking on some extra days and that the employee is using their holiday allocation and paying their accommodation fees etc then a good employer would normally allow this to happen.

Unfortunate not every employer is a good one!

I had a friend in a similar situation to the OP. They investigated flight prices and demonstrated that allowing him to tack on a few days of his holiday allocation would be hugely cheaper for the employer - as the trip then included a Saturday night stay - their boss still refused. The bosses boss when he found out was less than pleased that one of his managers had spent more than they needed to on the trip. My friend then took this as a sign (amongst others) that he wasn't valued so did indeed move to another organisation that was more enlightened.