Chlorine will oxidize the ammonia completely within a few hours, even with CYA in the water (unless there's a LOT of CYA in the water) and it is a whole lot cheaper than MPS. Usually MPS is around 3 times as expensive as bleach or chlorinating liquid or Cal-Hypo.
So that you can compare pricing,
one pound of 43% MPS (the usual concentration for Oxone) in 10,000 gallons is equivalent to 2.4 ppm FC of chlorine in terms of how much it can oxidize. I get 12.5% chlorinating liquid from my pool store for $3.29 per gallon (including tax) so to get 2.4 ppm FC in 10,000 gallons that requires 24.6 fluid ounces so costs 63 cents. One pound of MPS is 0.4536 kilo which you say is $3.50 per kilo so that's $1.59 for the same equivalent oxidizing amount or about 2.5 times more expensive -- so yes, your MPS is less expensive than most, but still far more expensive than using chlorine.
Also, the MPS noted above increases sulfates by 7.5 ppm while the amount of chlorine increases chloride (after the chlorine is used up) by 4.0 ppm.
When I had bacteria convert CYA into ammonia in my own pool, I used chlorinating liquid to get rid of it. It would have cost me a LOT more if I had used MPS. See
this thread for more details about my experience.
By the way, I'm not sure what was meant by "MPS reduces chlorine". It doesn't remove chlorine, but perhaps you meant that it reduces the need for as much chlorine for oxidation since MPS can oxidize bather waste (or ammonia) as well. It is not a strong sanitizer, however, so you still need chlorine anyway for that and would just add chlorine to maintain an FC level even if you were using MPS (this assumes you've gotten rid of the ammonia first). Anyway, I wouldn't use MPS to oxidize ammonia unless you had no choice or just preferred to spend more money.