I certainly think they should cut down on the amount of urgency. There should be times when you don't have immediate pressures on you. But at the same time, having some occasions with urgency is good for the story. It implies that the plot isn't just dependant on you - that the other players have agency of their own and can take actions of their own.
Presumably the ratio of urgent to non-urgent content would depend on the specific plot. Or rather, the plot should be written around the intended ratio.
Morrowind's plot, for example, handles this issue pretty well. The main plot in general isn't very urgent since Dagoth Ur looks to be decades away from finishing Akulakhan. There are two points in the main quest which should have some urgency. One is the period between being recognized as the Nerevarine and Vivec calling the Ordinators off. They can be pests; even dangerous at times -- though given the ease of disengaging from combat in Morrowind it's hard to be truly threatened, but if that's a problem it's a problem with the basic game design, not the plot. Corprus disease could have been threatening, but it isn't because the disease doesn't seem to actually progress; I'd have handled that part of the design differently.