It seems so strange that they’d offer X and just after being asked would switch to 4X. That’s a huge range.
Yes, I was surprised as well that they were willing to move that much. However, I know RSUs tend to be a lot easier to move on for companies than salary or bonuses (in fact, the salary offered was about 5% lower than my prior; I didn't even touch on that, instead looking to make up the difference, and then some, in the RSUs), and vary a lot more in the market. There are some companies that don't offer RSUs at all, pre-IPO startups whose grants are of questionable value, companies that grant RSUs yearly but only to a percentage of their employees, companies that give comparatively small amounts of RSUs to all their employees, and companies that give comparatively large amounts of RSUs to all their employees. That means the market range is huge and increases can more easily be justified; market range for salary tends to be far more constrained.
It's possible this may have also been due to being outside of SV; while the company has an office in my metropolitan area, I don't believe it's mostly dev, and while they have salary guidelines for outside of SV for dev, they may not for equity. So it may have been that the initial RSU offer was tailored to the locale, and my ask was okayed because it was in line for dev. Point still stands; they were incentivized to move, and they were able to. Had I asked at the start they would likely not have, simply because a recruiter isn't going to ask to make an exception for a candidate they haven't even interviewed yet.
Fair enough if you only want to work for a company that offers your target comp -without- negotiation (since even if they're open to negotiating at the start, you're doing so when your hand is weakest), but otherwise there is nothing to be gained by bringing it up at the start.