Knowing the amount of force that often is on my tiller, I wouldn't want to be relying on PU glue to hold it together where it previously broke.
As you note "properly cured" glue - depending on what kind of glue we're talking about - typically is stronger than the wood around it. That also requires a properly prepared surface for the glue joint, proper clamping pressure and proper (optimal) conditions (such as humidity, temp and cleanliness of the surfaces being glued).
And the fact that the glue is stronger than the wood adjacent to it means only that when the joint fails, it will do so adjacent to the glue line
, rather than on the glue line
itself. The wood adjacent to the glue joint will crack and split away and remain firmly glued to the glue joint.
It seems to me it depends on what kind of failure we're talking here (delamination versus a jacked, splintered break?).
But in general, if my tiller cracks or breaks, I almost certainly would just make another one - and perhaps reinforce the area down near the rudder head with a wrap of epoxy