Howdy,
This is an interesting question to me because of all the interesting mechanisms. The answer is less interesting, though: the average intake over time matters more.
In the very short-term (minutes/hours), muscle protein synthesis rates fall when they run out of materials, e.g. amino acids. This is one of the mechanisms that drives the “eat every 3-5 hours” advice.
In the short-to-medium term (days), total daily protein intake seems to matter more than how often people eat protein, or where they get their protein from (vegan vs animal vs mixed) when the intake is high. The definitive study hasn’t been done yet however, where people would have the same high (>1.6g/kg/d) protein intake, they would lift, and be split between 1 meal a day vs 3 to 5.
In the medium to long term (weeks to months), the performance outcomes we care about, strength, muscle mass, cardiorespiratory fitness, seem to track more with average protein and energy intake. In other words, a very low Calorie diet would still produce worse outcomes despite the higher protein intake. Still, protein matters, as a higher Calorie diet would produce worse outcomes compared to maintenance with low protein intake.
I think these all point towards the average protein intake, as well as the broader dietary pattern, as the key dietary factors related to training outcomes. I think a wide range of protein intakes work, where the “optimal” amount shifts a bit by person: leaner people need a little more, more training benefits from more, and lower Calories likely benefit from more.
As far as why…I think the best explanations have to do with the adaptations being discussed.The muscle you can gain per day, per week, and per month is on the order of grams, dozens of grams, and a few hundred grams. Strength also comes from more than muscle, things like neural adaptations and changes in tendon and ligament properties. I can’t see any of that being compromised by a daily intake that swings by a few dozen grams.
Further reading