Why is it not recommend to put V brake levers on cantilever brakes? I understand that V brake levers pull more cable out then cantilever brake levers. However, the argument why one shouldn't put V brake levers on cantilever brakes I often hear and also the only one I found by searching is that by doing that, you will not be able to create enough "power" to brake properly. This doesn't make sense to me, if it is true, can someone try to explain why it is true? The thing that does make sense to me is that by having that setup you will not be able to use the brake "half-way", that is, either it will be far from rim, or when you pull the lever slightly it will already be "very tight" to the rim braking "100%".
It's the old lever law: You can either increase force or movement distance at the expense of the other; the product force times distance remains the same.

The V-brake levers pull more cable, so they pull it with less force. If you pull cantilever brakes with a V-brake lever, that force reduction means that you get much less braking power when you put the same force into your grip.

Whether that's a problem depends entirely on you. I have strong hands, and I use good brake pads, so I can easily apply too much force on my V-brake levers, and consequently wouldn't hesitate to use it on a cantilever brake. If you have weaker hands, and/or worse pads, you may not be able to comfortably get enough braking power out of a V-brake-lever-actuated cantilever brake.