I have never carried my reels as carry on and i never had anything broken or stolen in the past 10 years. Not sure who you flying with but i went on Air NZ and had to buy an extra piece for my rods. So now i use 100mm pvc pipe with 2 rods and all my small stuff inside that pipe as it can be 23 kg. Poppers, stick baits and jigs also into the pipe. Just wrap in cloth or whatever. You can put alot of gear into a 100 mm pipe if want.
Just the way i do it.

It can be a bit hit and miss from what I've heard. Certainly hooks or anything with hooks attached are a no no. LIne can also be a problem so to be sure it would be best to remove the spools and place them with the non carry on luggage.

Also ensure your tube length is within the length restriction for the airline before it becomes oversized as it varies per airline and destination e.g. Air NZ 1.8 m length for domestic and 2m for international

I have taken plenty or reels and small hooks and small jigs in cabin. Never been hassled about fishing line. Tell them its no different than shorts drawstring. Aussie didn't like my big poppers with hooks. I believe 6cm is the blade size but countries vary. I had to tell them hooks were smaller than 6cm.

Also no problems with reels in hand luggage or rods in carry case in hold.
Once had an issue in the states with rod tube unit as my lock they had no key for. I had to open for them.
And if you didn't pick up on that, they have there own extensive range of master keys at most customs points so they can investigate without detriment to the luggage container.

Grunta - did they just question, question and verify it was okay, or restrict you taking it?