As others have mentioned, the big tech companies are all actively doing this. Nevertheless, it's not really taking. I know 3 people who moved from Google's NYC office (the 2nd largest) to Mountain View because all the top-priority projects were in Mountain View. As a general rule of thumb, you want to be where the executives are, and the executives are going to be at headquarters because a.) that's where their home is and b.) that's where all their most productive people are.
There's a steady conveyor belt where young single folks move from satellite offices to headquarters when they want to advance their career and then older folks move to satellite offices when they have kids, to be with their families or enjoy a better quality of life. This is healthy in the sense of maximizing happiness for everyone, but it means that the most ambitious, highest priority projects and most talented people are going to cluster at headquarters.
(As a side note, I feel like not enough people understand that the cost-of-living in SF is an effect of the wealth that's been brought into the area by the tech industry, and isn't just a random fluctuation. If some other metro area suddenly had a large concentration of successful companies that paid high wages, the cost of living would go up there too, until COL-adjusted salaries equalized peoples' preferences for living there.)
Satellite offices are tough to do right. It's very hard to build trust between individuals at the different offices without regular face-to-face contact. In the absence of this, you end up with negative relationships between teams at different sites: "The team in Springfield doesn't care about quality" vs. "Those Shelbyville engineers are always dragging their feet and never launch anything". Communication bandwidth between sites is also much more limited - you need to minimize how much a team at site A needs to communicate with teams at site B to get their job done.
Another issue is how to get the satellite office going from a cold start. Do you re-assign projects that are already being worked on in your existing office? Most of those employees aren't going to move, and they're going to be upset that their project was yanked away from them. You've also set the project up for failure because everyone on the new team has to ramp up on the necessary domain knowledge from scratch. So you think "Ok, I'll leave existing projects at the current office and start new efforts at the new office." Now you have an office exclusively working on things that were deemed to be either too low-value or too risky to work on before - not a recipe for success.
Leadership is another major issue. If your senior leadership moves to the new office, they're going to be constantly flying to the larger original office to supervise things there. More realistically, they're going to stay in place, because their time is better spent at the bigger office. This creates problems as leaders move up the ranks at the satellite office, because eventually they hit a point where their career stalls unless they move to the "head office". Teams at the "head office" are at a permanent advantage in project selection, etc. due to proximity to senior leadership.
In short, it's not as easy as your list makes it sound, and it's particularly difficult to grow a satellite office to a similar scale as the original office.
By growing any one of their regional offices, they could move their headquarters. Toyota recently did this over the course of several years. They announced the relocation in 2014, but didn't officially move the HQ until 2016. The planning and execution spanned years before and after that timeframe as well.
Or a required move.
A move strategy could be as simple as, opening up an office in a cheaper location:
1. New teams are created at the new location.
2. New hires on existing teams are placed at the new location, with exceptions if teams have a strong need to be in the same place.
3. Make it clear that you'll help people relocate to the new office if they choose to--some people will take you up on it.
Eventually, the original office will shrink and remaining staff can be allowed to work remotely (which should be a big part of a culture anyway, IMO).
Turnover is already high at tech companies, but in this case your turnover facilitates the move--as people leave at the old location you replace them at the new one. There will still likely be some turnover caused by even the slow move, but that turnover already exist with any move--even the move to south SF will probably cause some turnover because the location is just less convenient for some people.