Does it make sense to keep the launch of a rocket slow because the change in velocity (a.k.a. delta_v) should be as small as possible because of energetic reasons?
No. Nor the opposite.
Smallest possible launch useful speed is barely >0 m/s. The rocket will mostly hover, spending all of its fuel just fighting gravity. Inefficient.
The other extreme is almost an explosion. Tons of engines (weight!), huge acceleration and within seconds huge speed. And that means huge aerodynamic drag.
So we balance.
Launch as fast as reasonably possible, which means take in account
- Weigh of the additional engines, or bigger engines to accelerate faster
- Structural supports needed for high acceleration.
- The aerodynamic drag
Which most of the time results in:
- Launch fast. Engines at max.
- Reach high speed (at still low altitude, so still high drag)
- Throttle engines down to keep drag in check
- Once out of most of the atmosphere throttle back up.
And of course, all of this varies per mission with different rockets, different payload, different target orbit, etc. etc.
It makes no sense to deliberately keep launches slow. The slowest possible "launch" is a hovering rocket. It is 100% efficient at converting propellant into sound and fury, but 0% efficient in converting it to lift.
The faster the launch (up to the tolerance of airframe, payload and crew), the more efficient. In the case of airframe, this is "Max Q". For payload, electronics can withstand the acceleration in artillery shells. For crewed launches, maximum G-forces at launch are usually well below what is tolerated at re-entry.
Fundamentally, this comes down to fuel being cheap and rockets being a lot more expensive than fuel tanks.
If your rocket takes off fast adding a bit more fuel tank to it isn't going to cost very much, the additional fuel is even cheaper. You lowered the cost per kilogram of payload. There is an issue of diminishing returns but the optimum point is with the acceleration pretty low at first stage ignition.
There is also the issue that acceleration goes up as the fuel burns off. The higher the maximum acceleration the stronger everything above it must be, thus you have an incentive to keep the acceleration down. Few rockets have enough engines that you could keep the acceleration in check by shutting off some of them early.
Something that has been implied but not spelled out in the other answers. If you launched going 0 m/s upwards, you would literally be wasting all of your fuel fighting gravity, and go nowhere at all. Therefore, higher accelerations are better. Of course, there is a reason that rockets down accelerate at 1000G:
- Your fuel supply will be burnt very quickly
- You will lose a lot to drag
- You will destroy your payload
- You will destroy any crew
- The rocket will blow up from the aero-forces
- You will need a lot of mass for the engines
See Hennes answer for what we actually do and why. I won't repeat that here.
The other answers have quite clearly explained that, for a launch vehicle, launching as slowly as possible is inefficient.
But you mention 'for energetic reasons' in your question title: if you are, in fact, looking for the most energy-efficient rocket (rather than the most practical), the answer is slightly different.
The answers to this question explain this far better than I have been able to. My attempt to explain it is included below.
In this case, while you may still lift-off quickly, the velocity of your rocket engine exhaust should not (initially) be high. Decreasing this at takeoff is actually beneficial for efficiency (given a constant power) - so, in some abstract, tangential sense, your intuition about this is correct.
Consider: your rocket exhaust is moving very fast, therefore it has a lot of energy. That energy is wasted - we don't care about the exhaust once it has exited the rocket. If you tune your exhaust velocity so that the motion of the exhaust after leaving your rocket is negligible - in other words, the exhaust velocity is essentially equal to the rocket's velocity - more of the power put into the exhaust goes to the rocket, because the exhaust has minimum energy. For an explanation using maths, see this answer.
A more mathematical approach to this argument can be found in this NASASpaceflight forum thread, regarding exactly what effect a VASIMR-like engine has on the performance of a rocket.
Do note, however, that modern variable-isp engines are not particularly useful for launching a rocket from Earth. This is because launch vehicles are very mass-constrained, wanting to get as much energy out of each Kg as possible - they are not especially worried about being 100% efficient with that energy.