For me, it's quicker to grab my primary, duck my head and donate than to fumble for my octo (yes, I'm exaggerating a little bit, but I've been in that situation).
Of course this is very fast, and perhaps more safe for the receiver. What I am not sure is that this is also fully safe for the donor...
I have already read a couple of incident reports, in which, after donating the primary, the donor had problem with the alternate. Resulting in TWO divers in distress...
I remember that one of these posts was here on SB, the other was on an Italian forum. In both cases the result was a CESA, which is definitely not a nice thing.
If I find the SB post I will link it here.
To me, it happened at least three times of being asked for air, and I gave them my secondary (or my tertiary, when working I always employed also a full complete reg on the second post, routed the wrong way, on my left shoulder).
Never had problem finding it. Zero delay....
My wife, who usually closed the group, had many more cases than me, perhaps 12. It was very common at the time, as customers were given too small cylinders (10 liters), and someone going LOA was happening every 2-3 dives. In most cases this was happening at the end of the dive, during deco, and they could use the deco cylinders being attached to the deco rod, but sometimes it was happening at depth, and in this case the third reg with long hose on the wrong shoulder was perfect....
At the time no one was using a long hose on the primary, nor donating the primary was expected, so the customers LOA or OOA were searching for the yellow secondary or tertiary reg attached to our shoulder harness.