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.
Within two years of Gmail going viral people were screaming from the tops of any soap box, tree and mountain You are the product!! but as these things always go, very few people paid attention.
And not just a little bit of convenience. At that time, Hotmail had like 14 MB of space whereas Gmail had 1 GB. Before, you were constantly out of space, whereas Gmail users could keep on going without ever deleting anything.
Would you rather walk if you could have a personal uber driver with a Mercedes? Well, the driver is super creepy, but least the seats are soft. He will take you everywhere for free, but will also know everything about those rides and the conversations you had during them.