There was a real cost to printing single newspaper to me. I've no idea what it was, or is now, but it's about a million times more than the cost of me reading every new story on the NY Times website today. Maybe not a million times, but it's certainly much higher.
So while I do agree newspapers have always been ads with some news thrown in there to get people to look at the paper, there were some much higher costs there in the paper part of the newspaper (and printers and delivery people and so on). In theory the cost of how I read "the paper" now should be much lower, so if I pay to subscribe to the website maybe there shouldn't be ANY ads? Or far fewer?
I guess my thinking is nytimes.com isn't the same thing as The NY Times I get delivered to my house, so maybe things like ads should be treated in a different way? Sure the people that make it and reporters and news and all that are the same, but how I consume the actual thing is significantly different and has a different cost model.
Plus those print ads were/are WAY different in so many ways.