Yes nukes are as fast, or faster than warships and certainly merchant vessels. However the faster a nuke goes the more noise it puts in the water. Passive detection can pick them up pretty far away, also a nuke at high speed is reducing the effectiveness of its own sonar, and clearing baffles is a bigger deal. Nukes use max speed only to clear datum (and then go quiet), to evade attack etc. While speed is not relevant against active detection, it is key for passive detection. Submarines live by being invisible, put a lot of noise in the water and you might as well shine a spotlight.
For diesel-electric subs, run fast and deplete your batteries quickly, which could be suicidal. Using the snorkel and running diesels while submerged has limitations on how fast you can go based on sea state, and the more you run you diesels with snorkel the more time you are making a lot of noise. Running on the surface lets you get there fastest, and puts less noise out than submerged but still a lot, and of course you are visible to radar and the naked eye.
In many ways the transit from homeport to where you want to operate is the chanciest part of the journey for the submarine. Potential chokepoints and barrier ops, the issue of how fast versus how quiet and so forth.