Reading the replies it seems like this law may have incentivized some companies to make themselves extremely difficult to contact in the first place. How does the law deal with this?
Suppose I wanted to cancel a service from a firm that was hard to reach. I'd block the payments through my bank and if it ever went to court I'd just need to show I took reasonable steps to attempt to contact them before blocking any payments and then most likely win the case.
For many companies, there's just no financial incentive to let customers easily cancel or contact you once recurring payments are set up.
Ferengi Rule of Acquisition #1: Once you have their money, you never give it back