OK, first let me qualify this with what grasses and conditions we were using:

- irrigated (pivot) ground

- cut when in in head

- orchardgrass, timothy, garrison type grasses

These we'd cut leaving at least 3" of stubble. This resulted in faster re-growth, and with our short, high desert (6,000' elevation, 110 day) growing seasons, faster regrowth resulted in higher yields. The stand die-off started occurring when the stands were cut close on the last cut, leaving the grass with little means of doing root regeneration.

The time to fertilize these forage-type grasses with P is either at the start of the season, or by July. The root shedding and regeneration starts along about October. If you want to graze off the aftermath, you need to wait until about February; by this time, the plant has used up all the sugars, etc in the stubble for root re-generation and there's nothing left to it.

Alfalfa, on the other hand, you can cut shorter. The alfalfa plant has that big tap root in which to store energy; it doesn't care about stubble length. Where cutting too short does matter is when the alfalfa plant finishes one flush of growth (ie, the plant starts to flower), if you pull away the growth and look at the crown, you'll see the next round of growth starting up from the crown. If you wait too long, those new stalks get high enough you could start cutting them off. When this is done, then the regrowth time is extended on alfalfa. We'd always try to cut alfalfa in such a way that a) it would make test, which was usually 10 to 20% bud and well before the new flush of growth would start, or b) when it was in flower (eg, for retail horse hay) and just before those new growth shoots got tall enough to get clipped by the mower. Usually, I'd set the disc mower for 2". Too short, and you don't get enough air under the windrow, so 1. 5 to 2" is where I'd shoot for with alfalfa.