I have very little experience in aikido, having trained it on and off for brief periods as opportunity allows, so I may be way off the mark. Regardless, I'll chime in
The first few times I was nage for katate dori, I went fast and hard, and uke couldn't keep a grip. At first, I thought it was just that they weren't holding tightly enough or moving quickly enough. I figured that the faster I could go, the better, since I more commonly play at "hard" martial arts.
Somewhere along the line, I realized that I was off base. As nage, my goal wasn't to get my arm away, but to use that point of connection to lead uke through the technique. It seems obvious, but I had initially looked at the techniques as something to do to make them let go; that uke initiated the attack and I was defending against it with the waza. It seems to me now that I initiate the "attack" by inviting uke's grasp, and that my goal is the neutralization of the situation rather than just defensively "getting my arm back." For this, faster isn't always better; the speed and intensity of the waza matches the power of the attack. So if uke has a soft grip, I have to move in such a way as to keep that connection, so that I can stay in control of the situation.
It's like rythm changes in a striking art. Sometimes, you need to strike as fast as you can right off the back, to overwhelm the opponent. Sometimes, however, a slower attack or a delayed attack is better to draw out the response you need; to get them to committ and unbalance themselves. In striking or aikido waza, it seems that it's not more of any particular quality (speed, power, etcetera) that matters nearly as much as the appropriate amount at the appropriate time. I'm sure it's obvious, but for me there was a gap between intellectually "knowing" this sort of thing and internally "realizing" it.
Anyway, sorry for the rambling nature of my post. Haven't gotten nearly enough sleep lately
Hope some of it made a little sense, or was at least relevant to the question at hand.