A large part of my work as a legal recruiter is helping candidates move to a different geographic location, rather than switching firms within the same city, and quite often this involves a candidate moving from a large market.
Even though places like Phoenix, Seattle, and Portland are still major cities, the salaries on average are quite a bit lower, and thus there can be a little bit of a sticker shock for lateral attorneys once they see the actual number in an offer letter. For instance, the total annual compensation (base salary plus bonus) for a sixth-year associate at a big firm in a major market can exceed $250k, but that same associate would likely see a maximum total compensation of $200k in a best-case-scenario in Portland or Seattle - in other words, a 20% net cut, and the gap can very often be wider.
I always prepare my candidates for this reality at the outset of their job search when they are interested in these markets, because when I meet with recruiting coordinators from smaller market firms, one of the main things they emphasize aside from preferring candidates with strong local ties is that they need the candidate to be prepared for the lower compensation levels. Some firms will even bluntly ask at the outset if a specific candidate would accept a hypothetical offer in their standard salary range before proceeding with the interview process, which I think is very fair since there is no point in spending everyone's time if a candidate will end up insisting on an amount that is not in line with the firm's compensation structure.
It is certainly appropriate to negotiate for a stronger compensation package if you are a stellar candidate in a practice area with high demand, and I always try to help my candidates get the best deal possible, but the simple reality is that you will have to be prepared to take a hit in compensation when lateraling to a smaller market despite what you may be worth in a larger market or at your current firm. Even though a formal offer does not come until the end of the search process, you need to think about it very seriously from the start!