I would not categorically claim that a steady flow will give you a better shot, rather I'd say it gives you a more consistent shot; and consistency is highly desirable—if you can reproduce a shot consistently, then you can incrementally improve on it by tweaking one variable at a time.
Water pressure is a key variable in extracting the oils from the coffee, so if that variable is moving around during the extraction of a shot then you're going to get an inconsistent shot—it would be like mixing weak and strong shots and stirring them together.
If the flow rate is fluctuating then—I can't think what else it could be—unstable water pressure is the cause. Water pressure fluctuations could be the result of:
- the water pump is failing
- the water supply is restricted
- the (dry) puck is soaking (at the start of a shot the dry beans absorb moisture like a sponge so you won't see anything come out at first)
- the (wet) puck is channelling (water has found a path through the puck with less resistance and—like a hole in a dam wall—is rushing through it)
A variable rate of flow could get interesting if you have it under control and are experimenting with extraction techniques. You might try to slow it down toward the end of the shot in order to get more oils out, but I think this just makes it bitter because you're actually reducing the pressure—so it is self-defeating. Unless you have engineered a device which can detach pressure from flow rate... but now I'm dreaming... something like a camera shutter mechanism?