This happened to me, on an out of warranty 5D III. I took it to a Canon service centre. I was told the part costs around £2-£5, but the service centre would charge a minimum of circa £100 to fit it, including VAT and labour. They directed me to purchase the parts - black knob and rubber seal - from Lehmann's in Stoke. Lehmann's told me the rubber seal cost just 20p, but even though I didn't need it I would have to buy it. A day later, the knob and seal arrived, at a cost of £12. I put the new knob in, and it did not work.
I spoke to Canon again. This time I pointed out that its charge of 50x the cost of the part was outrageous, and that it should simply be fitting the part for free. I said if it did not, I would report it to the market regulator, the Competition Commission for exhorbitant charging. Clearly, Canon should not be fitting a camera costing £2,500-£3,000 with a cheap £2 knob, when that knob is going to be very heavily used, and that the loss of that knob is going to seriously compromise the functioning of the camera.
Canon responded by agreeing to try replacing the lost controller for £40.
I took my camera back to the service centre. Canon wanted £40 to replace the controller, to cover the cost of labour. I refused. This was now my second visit to the repair centre, which has a cost to me. Clearly, the Canon Mark III is poorly designed, with an essential part costing £2 that has, for a number of users, failed. That's a design issue, not a usage issue. There was no way I was going to pay £100 to cover Canon costs after having paid £2,500-£3,000 to buy the camera, when that cost arose from Canon's poor design and quality control.
I also pointed out that I had bought an expensive pair of BOSE headphones (QC 25) at the same time as the camera. I'd had many issues with the headphones over the years. But, each and every time, without fail and without quibble, BOSE replaced the faulty part. I pointed out that this gives me confidence to buy BOSE products in future, because I know I'll be taken care of should anything go wrong with the product. I said Canon giving me the run around, wanting me to visit them up to 3 times (they had wanted me to leave the camera with them), sending me to Lehmann's for a cheap part they had upstairs and could have fitted for free on my first visit as a goodwill gesture, just created a bad impression.
Canon relented. They took my camera and replaced the missing multi-controller. Apparently, inside the black knob, there was a missing mini white stick, which Canon had not told me I needed to also get from Lehmann's. I saved myself £100. But the big picture here is that I don't think any Canon Mark III user should ever agree to pay Canon £100 to replace a £2 knob on their camera. It's a Canon design fault, not a usage fault. Design the camera better, and use better quality parts, and the problem goes away.