I was on the phone with a cstomer service agent, and he said repair costs for a 3DS XL is $130 + the shipping you'd have to do. Thats $130 for a $200 system for an issue thats probably very minor.
Without knowing the specific issue I can't speak to it specifically, but I will tell you from my experience buying up broken systems and trying to repair them for fun that you would be surprised at how expensive 3DS XL parts still are. Most of the time, it is just not worth repairing at all.
For example, one of the most common problems I see with broken 3DS XL systems on ebay is a cracked top LCD. You can buy a replacement top LCD, but they are prohibitively expensive and require dealing with manufacturers in Hong Kong: cost about $70 or more plus shipping from Hong Kong, so right around $100. Even purchasing in bulk (we're talking hundreds bulk) the screens go for more than $50 each plus shipping. Factor in your time to take apart the system and hope you don't break anything else in the middle of your repair, and $130 or more for a repair of this magnitude makes sense, even for Nintendo.
Other parts are cheaper to replace, but only if you can find them. For example, there are no aftermarket replacement shells for the 3DS XL right now, only cases. You would have to salvage shell parts from another system, and they wouldn't be in "mint" condition. This is one area where Nintendo has the advantage--I'd like to think they have plenty of spare shells on hand. But even with a shell-swap, you might think it's an "easy fix" or "minor issue" but I assure you, it's much more tedious and delicate a process than you might think to perform. I challenge you to shell swap a DS Lite, which is EZ mode, and then move up to a 3DS, and when you're done with that, keep in mind that a 3DS XL is even more complicated than either of those. It would give you a new-found appreciation for the hardware and the cost of repairs.
Now I'm not certain at all how Nintendo's repair service operates, but from their perspective, even though parts are easier for them to come by, until you get the system in your hands it's difficult to know the exact condition of the system and figure out precisely what parts you have to replace. So what I am assuming happens is they have this blanket repair cost of $130 for the system which should cover pretty much any repair, including a major repair like top LCD or motherboard replacement. Maybe that's why what they quoted you was so high? I don't know.