You're omitting the likelihood that your applicant pool is tainted by compensation that's not inline with what your desired candidates want. (Note: this is not the same as what comp firms tell you is the 85th percentile or whatever.) (I know, you're "generous" for the market, which also claims a talent shortage and may have the same problem.)

But...approaching the edge case, do you think you would see more qualified candidates in your applicant pool if you advertised & offered a $1m/year package for the positions? Have you tried advertising the positions at double (or triple) the compensation to see if that changes matters? If you didn't test this, how do you know that the applicant pool has nothing to do with what you're willing to pay?

I'm here in Atlanta, and I can cite examples of people leaving for SF because their expected compensation goes up by a triple-digit percentage (sigh, candidates ignore costs but that's a different story). This effect changes the applicant pool in SF, perhaps boosting comp by 100%+ would work for your company locally? Certainly poaching talented employees gets easier when you offer a raise of $100k to join your firm.

Put another way: why would employment be different from other supply/demand markets where price matters, even if the price being asked is potentially distasteful to the buyer (see TSLA, AMZN, TWTR, FB, NYC apartments, or the flavor of your choice)?