We culled hard for years, didn't do us a lick of good, we had mineral deficiencies that were the root cause of it and I'm sure we culled a lot of otherwise good cows.
The key to a tight breeding season is a BALANCED mineral mix... If you're seriously deficient in anything, breeding is probably the first thing you'll suffer on.
BTW, Alfalfa doesn't have much phosphorus in it... In hay, they say it's 1.5% Ca, 0.3% P, and 0.4% Mg. In contrast, Barley Silage is 0.5%Ca, 0.3% P, and 0.4%Mg... Barley as grain is 0.06% Ca, 0.4%P, and 0.2% Mg...
So Alfalfa has a 5:1 ratio, which is a bit steep on the Calcium side... Meanwhile dairy cattle that eat a lot of grain get tons through it, and need more calcium... part of the reason they get milk fever more than beef cows (Magnesium is part of that equation too)
Obviously the ground the food was grown on is going to contribute to those numbers.. seriously P deficient soil will probably not have as much in the grain either.
Another note,.. High calcium reduces phosphorus uptake, as well as a Vitamin D deficiency... some points to keep in mind too.
If you want some reading material... I spent a lot of time researching this.. Here's a link to the thread
viewtopic.php?f=7&t=73928