Sometimes you don't have the option. Usually you can't book those seats with online checkin. And the people at the checkin counter will be allowed to give you the emergency exit or not based on what category of ticket you bought. If you bought the ticket with a very low price, a special offer, etc. you have low chances of ever receiving any upgrades. If you paid a full price within the same class you may get something.

Most of the times when I showed up with a full price company bought ticket (coach) they would offer an emergency exit seat even without me asking. Almost never when I traveled privately with the same airline but bought the cheapest coach tickets I could get.

Sometimes I fly low cost because I know I can get the extra leg room with minimal hassle.

Sure, but that's besides the point (and not applicable for personal trips). Should I (or my employer) have to pay more money to get reasonable accommodations on a flight due to my physical nature? Surely there would be an uproar if an airline started charging extra for accommodating people with disabilities?