Thanks for the feedback, all. Lots to consider.
I want to stick with the convenience of an unmodified milk crate. I can dump a wide range of things in there, it doesn't bend, and doesn't rattle, and the high sides are secure for large grocery bags or an upright backpack.

My new commuting bike has 26" wheels, my stem/bar clamp would be above the edge of the milk crate, and flat bars won't interfere with a milk crate by sticking forward (as mustache bars do) or forward and down (as drop bars).

I fully buy the low-trail-for-front-loads line, but I'm not sure about the head angle and trail characteristics of the bike. Mid-80s lugged Panasonic MTB. Probably a slack head angle like other MTBs of that era. Not sure about fork rake/trail.

That said, even when not considering steering geometry impacts, a basket over the front wheel has the following undesirable characteristics.
* the basket would sit ahead of the axle (as measured along/parallel to the steering axis) and so would affect the steering even if the bike had proper geometry. Unlike typical handlebar bags (or baskets that don't stick so far forward).
* over the rear wheel, a load shifting around in the crate doesn't meaningfully affect steering geometry. However, backpack of groceries shifting in the front basket could affect handling. I'd prefer not to muck around with bungee cords, and have never had to with the crate over the rear wheel.

So, odds are I will stick with the crate over the rear wheel.