Measuring the temperature of the heater is not really measuring the temperature of whatever it is you are trying to control. I'm also not sure the Kanthal elements will last all that long if you're operating that close to the maximum but it really depends on the atmosphere they will be exposed to. You also need to find a way to calibrate it (a thermocouple or an optical pyrometer) and 50ppm/°C means you will have trouble with tight control. I think it can be made to work at least for a short time (without my doing a lot of evaluation of your proposed method) but I don't think it will be comparable to a thermocouple controller unless you have a very special need to control the temperature of the heating elements themselves.
A not insignificant problem is that the resistance and the elements themselves will change significantly during use so that your actual controlled temperature will drop continuously as the elements erode away and the resistance increases.
A standard platinum-rhodium thermocouple can easily handle those temperatures (type R or S are most common, and work up to 1450°C). They don't have to be fat like AWG 8 thermocouples, even a fine wire will last a long time, because Pt is very non-reactive ('noble'). The output is quite a bit less than common base-metal thermocouples such as K or N type, but still not a problem for modern electronics.