Not sure how this applies to "30 years" of "IT BS". Previously, with shrinkwrapped, if you bought something, and it worked fine, you were in a position not to upgrade, and not have to pay for it. And if it works fine, you don't need support for it either. (this, of course, ignores the network effects of everyone else upgrading other than you, which forces you to, but this is not the provider's fault, other than creating built-in obsolescence).
Now, you maintain a relationship with the provider of your web-based software (one could argue that Internet Explorer does not provide a good "web" experience because it is so broken), it doesn't come in a shrinkwrapped package that you install and use. How this is different from anything else the customer owns is that the customer doesn't own anything in this case, they are paying for a service (technically, because of the law and license agreements, they don't "own" shrinkwrapped software either, but that's a side point). The service they were paying for ("ability to use the service on IE6") is disappearing. It's not economically viable for IE6 to be supported anymore (especially for user who are not interested in paying for maintenance) -- are IE6 users part of the long tail?
It's not 37signals that is forcing you to upgrade to use their service. It's Microsoft, who wrote the busted browser to begin with. It's also Microsoft for not easily allowing multiple versions Internet Explorer to co-exist on the same computer, thereby making upgrades more difficult to people to deal with.
As for if it is a benefit for the supplier for the customer, it's a benefit for both. Customers get a better, more consistent experience (including features deployed faster, quicker load times, both because there is less code to maintain), and suppliers do less work for providing the same kind of product.
(obligatory car analogy) Does anyone complain the same way about parking garages that have height limits, and about how they are losing customers because they don't cater to customers who drive oversized vehicles? They just choose not to support the incompatible customer.