I agree with you - processed meats are generally terrible for you, and the line that they're doing this for the climate is utter bull.
Processed meats are not just hot dogs and bologna. It includes things like bacon, salami, corned beef...
However, there is more to this move than banning processed meats. The city is going to eliminate half of ALL red meat from city facilities. Yes, that doesn't include privately-owned restaurants - one of the stellar draws of NYC, in my opinion - but I'm sure they will feel after-effects of this, as well.
I have no problem with someone choosing a vegetarian diet, or a omnivorous diet, or really - any diet that excludes cannibalism. But I twitch at the idea of the government mandating what I can and cannot eat.