Parmandur
Book-Friend, he/him
In practice, it's pretty difficult to run anyone out of resources in a day, unless the DM is intentionally going over-and-beyond or the players are being extremely reckless.
By the time a fighter has more attacks than the barbarian, the barbarian has four rages per day, and gains a fifth at the following level. While it's possible to fit six encounters into the daily XP budget, most of them will be on the easier side, and nobody needs to expend a limited resource on an easy fight. While the fighter may be the star of show in easy encounters, the barbarian will have more than enough juice to steal the spotlight in any fight worth talking about.
So, apparently, the expected range of actual play based on playtesting is 20 rounds of combat across 6-8 separate encounters between long rests. Certainly the game isn't limited to that, but if you aren't even pushing the resource game to the limits things will be off.