So even militia were normally armed with a cartridge box of some sort. "Independent fire at will" was more of a rifleman thing back then and the riflemen had the time. The men with muskets would fire at a rate that we would think was "slow", and move to load upon command, so even those with horn and ball had time:
Archive of Maryland 1775-1776
And therefore it is recommended to such of the said in-
habitants of this province as are from sixteen to fifty years of age,
to form themselves into companies of sixty-eight men; ...,
and use their utmost endeavors to make themselves masters of
the military exercise: That each man be provided with a good
firelock and bayonet fixed thereon, half a pound of powder, two
pounds of lead, and a cartouch-box, or powder-horn, and a bag
for ball, and be in readiness to act on any emergency.
That every non-commissioned officer and private of the minute
men and militia appear at the time and place appointed for their re-
spective appearance, for mustering, with his firelock and other ac-
coutrements in good order, and there orderly, diligently, and obe-
diently attend to instruction, and perform his exercise in arms, ac-
cording to the commands and orders of his officers, and if any min-
ute or militia man shall not appear at the time and place of muster
with his firelock and other accoutrements in good order, ...,
he shall forfeit and pay a sum not exceeding five shillings common
money for every such neglect or misbehaviour,
Emergency loading of a musket when one does not have a cartridge is done as was mentioned. Cup the ball in the palm of the left hand and pour powder over it to just cover it. Use the left thumb to hold the ball in place, and pour the powder from the hand into the barrel. Then release the ball and let it drop into the barrel. Ram it home. Then prime the musket pan. So that's a form of "eyeballing it" but not direct from horn to muzzle.
When you don't have enough time to do a proper measure of the powder that is also the WORST time to be trying to pour from the horn directly into the musket, for that is when you are most likely to have fired several previous shots, and to have an ember within that will blow you up when it cooks off what comes down the barrel.
Further, IF you're providing your own powder, you do not want to dump it willy nilly... it costs money, and some method of regulating it means you have live ammo as long as you have ball. Pour too much and you're out too soon, and then you're down to a bayonet vs. professional bayonet fighters aka Redcoats.
LD