Submarines prefer "sprint and drift"? Why would you possibly do that in a submarine if you already have an advantage? Surface ships, on the other hand, can benefit from this tactic because 1) a sub tracking a ship would have a tougher time getting and maintaining a firing solution and 2) if a sub wants to keep up with a surface ship, it will have to increase it's own speed (read: become noisier and hamper it own detection capabilities) and if the sub does not time its own stop from the sprint then you will have a surface ship already in a drift listening attentively if anyone is chasing it and the sub chugging along giving itself away. That's not even considering the option of a anti-sub helicopter sitting around and waiting for the sub to make its move, or two ships working in tandem, or two ships and 1-2 helicopters...
I think you're only considering the scenario where the submarine is close to hostile surface vessels.
If a submarine has to cover a distance safely and quickly, depending on the threat situation the commander might choose one of a variety of options
Let's take a look at a scenario where the submarine has to cover a distance of 100 nm
1) If the commander covers the entire distance at full speed (30 kts) he can probably reach the destination in 3.5 hours. But he will be completely deaf and blind for the entire trip.
2) The safest option is to proceed at his best quiet speed (5 kts) but then the journey will take 20 hours
3) If he sprints (20 kts) and drifts (5 kts) for alternate half hour segments then the entire journey can be completed in 8 hours while still having a decent idea about what's going on around the submarine.
When close to a surface ship then timing does become a problem, but that's where the commander of the sub has to make a judgement call. He can either continue running slow and silent and risk loosing out on a target or take a risk and sprint for a short while to get to an unexpected position. Flow noise takes a while to settle down as the ship/sub reduces speed and a submarines is usually in a better position to detect whether the surface ship is coming off a sprint and reduce speed accordingly.
Multiple assets prosecuting a submarine does not necessarily mean that the sub has no chance. The tactical situation will depend on a lot of factors, the nature of the threats and so on.