If Gmail proved anything, it was that people would, for the most part, accept any terms of service. Or at least not care enough to read the fine-print closely.
Gmail wasn't even the first, Hotmail, Yahoo mail, there were tons of free email offerings, even sites that would host your whole website for free like geocities. Gmail came into the market when 3rd party email being free was already well established. They just followed an Apple style of development, taking something that already exists and made a better version of it. Also back then their motto was still "Don't Be Evil" and they mostly still kept to it, so they used that goodwill and the better user experience to grow it at a massive rate. And for the most part, its still the best experience for email for many cases.
I remember the counter too. The ever growing available capacity of my mailbox that was more space than I could ever use. Just open Gmail and watch that number grow