Extra seat for instrument
[EDIT: I insisted on the service line that this issue should be sent up the chain to be solved for the future, and apparently it was sent up to "the team of experts" who analysed the proposed booking and said it indeed made no sense. They were able to create a booking where the extra seat is at 75% of a regular ticket price, and also without any of the taxes and fees that apply only to passengers.
So for people facing that situation in the future, apparently we can (and must) insist that it be reviewed, so that a normal price is offered!]
Putting this here in the off-chance that someone from KLM reads it, or that someone has an idea of how to raise the issue with KLM so that it gets solved in the future (guy on the service line was thoroughly unhelpful and said there's nothing he can do and it's just the way it is, and couldn't think of a way for the issue to be elevated and maybe eventually solved...)
When needing to carry a large musical instrument on board in an extra seat, KLM requires that both tickets (for the passenger and the instrument) be booked by phone. I tried to do that, but the price they quoted was nonsensical.
Price for a single ticket for the route on the KLM website : 197€ (and also 394€ for two seats).
Price for 1 person+1 extra seat for musical instrument on the Service Line : 1016€ total. Assuming the price for the passenger is the same, that means 819€ for the extra seat, or a 315% surcharge on top of the regular ticket price (in practice actually more, because some taxes and fees that the airline charges you but doesn't pocket only apply to passengers, not to items in extra seats)
I can't imagine that this is actually what KLM intends for its policy, 1) because they're actually very good with musical instruments in every other ways, 2) it wasn't like that last time I asked, it was just the regular ticket price, 3) it just makes no sense whatsoever, because nobody will pay that price for an extra seat. I'm certain it's a problem in the algorithm used by the booking system, that people in charge are probably not even aware of.
Just to be clear, I'm not complaining about or hoping to solve the booking I wanted to make (I'll just book other travel arrangements), but hoping that someone has an idea about how to bring up the issue with someone that can actually look into changing it in the future for something that actually makes sense.