Glacier travel/ snow with one axe and a ski pole

Curious what others thought. Just got back from summiting remote peak with internet partner found at last moment. Always happy to summit and partner solid in sketchy 4th class stuff.
Partner used one ice axe and one ski pole for all of snow/glacier portions. Not a very intense climb with good conditions - snow to maybe 40 degrees. Got impression that was partner's preferred technique for all mountaineering.

I know occasionally people have died on Denali pass cruising along with ski poles and crampons (I've seen the practice myself there). Only found one similar thread (titled "Does anyone actually use a mountaineering axe?").

Here is my question - What do you think of using one ice axe and one ski pole on glaciers and 40 degree snow (or in general)? To me it just set off instinct alarms. I could buy the argument you might be slightly less likely to fall with the extra support but if you actually do fall I think the chances to self arrest are much lower (the brain would have trouble letting go of the ski pole quickly).

Didn't really discuss with partner. On this particular climb I wasn't that concerned. This is more of a general question. I would think the steeper the snow the higher the risk with this technique.

For easier glaciers and snow, I generally use a light pole and ax. I do not stick my hand all the way through the wrist leash though as I don't want it to interfere with an arrest, taking extra care not to drop the thing during general use. I stash the pole during spicier sections. I have no problems with experienced partners using a pole but I'd prefer if newer partners did not as they've got enough going on figuring out prusiks and slack and not tripping over everything (like their prusiks and untidy slack).

Were you roped together?

This is how I do it and how I was taught by a guide at AAI. Had to arrest a fall, didn't have an issue dropping the pole. I don't use the wrist leash though, and you probably shouldn't at all either, it'll slow you down every time you go to switch direction.

Just use a whippet (or two).

Yes - we were roped together.

An axe and pole is SOP for me and my partners. Ya learn to do the shuffle and you can move up hill much faster than with just an axe. When the pole gets put away all depends on the slope and conditions.

In my experience its more comfortable going up but sometimes feels scary on the decent. What I personally would like to hear about is this:

Lou Hibbard wrote: Just got back from summiting remote peak with internet partner found at last moment.