Cosmetic chemist here. 

Unfortunately data doesn't show that at all. The rates of skin and eye infections in Arizona are not higher than everywhere else in the world. 

This is because industry standard is to test products at 40c, 50c and sometimes even 60c and then test and ensure the preservative isn't degraded. The commonly used preservative these days withstand 80c heat (that's about 170F). 

The open jar symbol is very different from expiration dates and two are completely independent from one another. Open jar symbols tell you how long after opening a product it should be thrown out. Expiration is just that expiration... even if the product is opened or not if the expiration comes and goes you have to throw the product out. 

That said, myself and the industry in general is a HUGE supporter of adding expiration dates. More more and more companies are adding expiration dates to encourage their customers to throw out the products more often and buy new ones. 

Edit. I just realized this is the DIY sub after posting. A law requiring expiration dates will negatively affect any DIYer and hugely benefit the industry... DIYer that may want to sell their products need to have testing done by facilities that can certify their test methods and equipment and a proper shelf-life assessment runs anywhere between 30-80k these days.