I worked for a company that did just that: open an office in Canada in the same timezone as their American HQ to cut cost. The taxes, expenses, and complying with local laws at large scale (think: Quebec language laws) are real, and they almost ended up killing the office because the cost was too high. They absolutely were hiring more in the American office in the end from a pure cost perspective, and using the Canadian one to scale even though it was super expensive to run.
Now, its very likely it was them simply being inefficient and unprepared for it, but it doesn't really matter: its a real issue.
Now in the case of my current employer, we absolutely have international offices where getting head count is much cheaper, but to scale, we need offices everywhere where there's talent, and that includes in the big american metros. In my case, I just moved to get the $$$ of the American offices, that's all :)