You can increase productivity if you fire the right people
One thing I've noticed in my years of consulting is that something like 3/4 of the work is completed by the top 10% of employees, and maybe half the work is completed by the 80% in a wide 'average' range. Wait, you say, that adds up to over 100%, that can't be right! But it is, because the 10% of bottom performers manage to do negative work - their "work" causes more work for others!
They write bad code that takes forever to debug or has to be thrown out and rewritten from scratch. They fail to follow corporate or industry accepted standards and cause "should not happen" problems when assumptions are made that standard practices were followed when they weren't. They distract others and keep them from doing their jobs. They create chaos and play power games that derail projects.
I haven't ever consulted for a Facebook, Google, Apple, Microsoft, etc. so I don't know if this is true in the tech world elite. I've mostly consulted for Fortune 500 companies so they can afford to hire some very good people. The 10/80/10 split seems to be universal in my experience, maybe it is 20/70/10 or 15/65/20 or something but it is along those lines everywhere I've been.
So you really could improve productivity while cutting costs if you could get rid of the RIGHT people - those doing negative work. The problem is half of them are in management, or are team leads angling for management, and the political games they play allow them to point the finger of blame at innocents who get fired instead.
Sometimes even the top performers are let go in situations like this - if they won't kiss the boss' ass or allow him to take credit for their work. I saw that happen once and passed his name along to someone I knew who was looking for a contractor with his skillset and he doubled his salary overnight.
My consulting contracts prevent me from trying to hire or recommend employees of the company I'm consulting for, but when they are former employees it is game on! I made sure the manager who pushed him out learned he was now making 50% more than him. He tried to get my contract terminated based on getting a contract for a former employee but the HR person who handles contracts told him to pound sand lol!