No one is proposing public funding on a level that would build the hundreds of thousands of homes needed. It’s not a choice between a public and free-market solution. It’s a choice between setting a different goal for the regulatory climate (maximize units vs. preserve small-town character) and implementing token feel-good measures that help a couple thousand people at most.
In other words, given a choice between building 1,000 market-rate units and 200 BMR, or building 100 market-rate units and 100 BMR, she'll pick the latter.
[1] http://kalw.org/post/mayoral-candidate-jane-kim-takes-afford...
As predicted by the city economist, after this passed we saw a huge drop in the production of both BMR and market-rate units: https://medium.com/yes-in-my-blog-yes/the-25-inclusionary-ra...
Your second citation is anonymously written and of questionable quality -- check the comments.
[1] https://hoodline.com/2017/05/supervisors-reach-compromise-on...
Like @raldi notes any apartments -- of any height ! -- are illegal to build in 78.6% of SF: http://sfzoning.deapthoughts.com/ . what are her solutions to fix this then?
http://www.sfexaminer.com/sb-827-postmortem-lets-build-housi...
"A study by the city controller found that a rate higher than 18 percent would likely slow housing production and reduce the amount of subsidies for affordable units."
"Even with the reduction, the levels are the highest concessions required for affordable housing among any major city in the United States."
"Peskin and Kim had pushed for a 24 percent requirement"
"To date, only two single-building projects without public subsidies have agreed to 25 percent affordable housing"
https://www.bizjournals.com/sanfrancisco/news/2017/05/18/sf-...
And none of that supports your exaggerated claim that Kim would prefer 100 units over 1,000 units. She's overseen the construction of the most housing in the city.
[1] https://48hills.org/2017/03/real-facts-affordable-housing-de...
Even 18% (now 19%) can't be done at the majority of parcels in the city. I guess it's fine for SOMA, which has the highest land values and transit connectivity of any part of the city, but it doesn't work elsewhere.
The only quote from Kim is this: "If I’m going to give you ten additional storeys, I’m going to want you to increase your middle-income housing programme."
You can debate whether a purely free market approach will address this effectively, but it's inaccurate to characterize fighting hardest for low- and middle-income housing now as a "cooler approach". Cities need housing for service industry workers -- especially as more professionals move in.