This is tricky. She is still paying for it because when she buys a box of cereal from the store, X% of the price goes to the ad budget, Y% of which goes to Google, and Z% of that goes to the Chrome developers. She also pays by getting a lower wage, because if most of the people
had to pay $1/month for a browser, the salary cutoff point, beyond which people would simply not want to work, would be $1 higher. And then through supply/demand, it would slightly raise the average salaries. And, BTW, she would have one more opportunity to save money by not paying for a browser, and instead reading from a library computer. Or maybe using a cheaper volunteer-maintained Linux-like browser.
The thing is, money is just a token of passing value between people. If Alice is developing the browser and Bob is using it, there will be a mechanism to pass value from Bob to Alice to compensate for it. It can be either straight-forward (putting Bob in control) or centralized (through some social program, or ad revenue or whatever), but there will be one. Otherwise, Alice would spend her day playing ping-pong with friends, or cycling, or whatever people do when they don't have to work.
BTW, I do think that many social problems we are recently facing come from the fact that people are getting more disconnected from consciously producing value. If the abstract mother in Bronx had a clear path to making more money by opening a business and selling something to others, she would take that chance. And she would happily grow as a person and respect others who went the same path, regardless of their skin color. Except how many % of your monthly budget have you spent on owner-operated businesses vs. sector monopolies that treat people like drones and de-facto discourage professional growth to keep people more replaceable? That might also answer the question why the median salary in most areas barely covers rent, while the stock market is record high. Except instead of asking those questions and finding a way for people to contribute value in each others' lives without middlemen, we are turning tribal and trying to blame races, genders and political affiliations for a problem that truly affects us all.