I did a survey awhile back regarding the average number of combats per day and the those who said that their table averaged 3 or fewer combats per day were more than double those who said they averaged more than 3. Every other online discussion I've read regarding the number of combats that tables see lined up pretty well with those results. I'd say that across all of the tables I've played at, we average 2 fights per day and often none at all (while still blowing spells and resources). 2 refreshes per day would exactly meet the 3-combat-per-day average, so you're spot on.
When I first picked up 3.5, one thing that a realized early was that resources like the barbarian's rage that became more plentiful as levels progressed were awkwardly designed for actual games because of one emergent play reality: I saw that high level parties didn't actually engage in a greater number of combats per day than lower level ones, only higher scale ones. In theory, I like the idea of using PB to determine a recovery mechanic, but I feel that classes like the fighter, monk, and warlock are going to need a hard retune so that recovering twice per day when facing level-appropriate threats is balanced against recovering 6 times per day while likely facing the same number of challenges. It could be doable and is worth experimenting with but it's going to take some playtesting.