we have different chassis, different engines, different fuels, lubricants, we had different KERS-es... all of them are differentiators, so why not to have different tires ?
reducing costs skyrocketing does not have to be so complicated. rules could define max number of tire specifications each supplier can offer for the season, changing them during the season could be banned (changes could be made only on the ground of safety/reliability and have to be agreed by all teams, similar like with engines). we may even still have a two tire type per race rule in place but it could be up to each team and its supplier to decide which two to use. etc, etc...
at the end of the day it's all about competition and extracting us much from the limitations dictated by the rules as possible.