It all comes down to whether people will actually pay or not. Wikipedia runs off donations but they still get a lot of slack when it comes to their yearly banners asking for donations. Whenever NPR asks for money, it annoys users similarly. Would people be more or less annoyed with them if they had a ton of ads?

Both wikipedia and NPR are also lucky because the people who see their value are the same people who have money to donate. Facebook and Twitter aren't so lucky. Social media managers and companies will shell out a monthly fee for services like HootSuite so hypothetically, if Twitter/Facebook added features for companies, they could sell that service. Unfortunately, the goal of the company then switches from providing Facebook/Twitter to consumers and providing additional services for social media managers and brands. Whenever this occurs, the service is no longer as valuable to consumers and subsequently, the brands attempting to reach those consumers.

I've often thought about what would happen if Facebook attempted an advertising or donation model: if I donate $X/month, I wouldn't have to see ads. The problem is: the value of the ads is probably more that what I am willing to donate. Furthermore, if the donation model takes off, the price of the advertisements heavily declines. If a majority of your target demographic is donating to Facebook to hide the ads, why would you pay to attempt to advertise to them?

The biggest challenge with monetization of community type sites is that in order to get new users you have to focus on the people and the community. If you start giving people who pay a bunch of features, those who don't pay will be left out. If they are left out, you can never turn them into paying customers. Donations take away the direct need for two separate feature sets but, as there is no real incentive for donating, you better have a ton of people who love you or a noble goal to make it work.

I'm a bit troubled by this automatic assertion that web platforms should be profit-maximized

If you, as a consumer, want something amazing, amazing people have to spend an amazing amount of time building and maintaining and updating it. Without profits, those people can't put 100% of their time and energy into the product or service. Profits enable people to work on the project full time and continue adding features month after month, year after year.

If Facebook was given X dollars/year to keep the site up and running, do you think they would be take the time to develop a completely new mobile app? Do you think the UI would have gone through so many different updates? It would probably look exactly the same way it looked when they started receiving the public funds. It could've never scaled to the size it is today without the profits and possibilities as an incentive.

It would be interesting to see where libraries would be today if they were run for profits. Can you imagine the services they would be forced to provide to stay up to date, relevant and keep the money flowing in? I don't know about your library, but we still have CRT monitors in mine.