"I would recommend to gbaike that he considers three technical aspects of his augmented launch system:-

1) If initial impetus is valuable, then why do no existing launch pads involve springs, counterweights, pistons, compressed air, or other ways of "pushing" the launch vehicle the first few metres or tens of metres?"

Well I would not consider anything under say under 50 mph as not very significant in this regards. To get a rocket to 50 mph at 1 gee acceleration requires about 60-70'- or lifting rocket about 6-7 stories high in about 2 seconds- fairly daunting task to do with springs, pistons, or compressed air- though a rocket sled on a highly inclined ramp could do this.

A few other things to consider, is that rocket use for vehicles is relatively new and mostly something done by govt. And it comes directly from a weapon system- which really hasn't had much change to it from first German intercontinental rockets.
Another aspect is the pipelauncher is a ocean launch system- and Sea Launch is fairly new and is only one effort in this area.
Sea launch is the only private space rocket launch facility in the world. So I have a question why does only private launch choose a ocean? Whereas there numerous govt launch sites and they are all on land?
And finally one has consider recovery of whatever thing you using- recovery for this type thing in the ocean is generally easier than land.

"2) What is the initial thrust in g's of a real rocket leaving the pad? - this is important since your system must offer a comparable acceleration in order to be of value. The space shuttle pulls about half a gee off the pad, for example. Does the scale and design of your system provide this much acceleration?"

A pipelauncher would require less length if you could accelerate the rocket faster. For example in above with 1 gee with distance +60' if at 1/2 gee it requires about twice the distance +120'.
If the pipelauncher is 300 meters in length and max possible gee of 5 m/s/s that means it would accelerate for 10.9 seconds- lets say 10 seconds so that is only 50 meters per sec [112 mph]. If instead the rocket could withstand 30 m/s/s that allows same length of pipelauncher to give 132 meter per sec [295 mph]. If a pipelauncher were launching sub orbital craft these might be more likely to be able to withstand these types of higher gees.
A pipelauncher could be designed to be able launch a wide variety of different launch vehicles but obviously it could be designed to be more efficient if it was designed for a specific type of launch vehicle.

"3) How much launch mass savings does your system afford? If this is so critical, why do we not launch all rockets from the tops of high mountains?"

The main near term value of a pipelauncher is as being a launch pad. A launch pad in the middle of the ocean- in area where there are not fishing boats or cargo ships, not many surface fish, not many birds. And on the equator. And perhaps somewhere where you can launch on average 300 days of a year.
Mountains are generally not near the coast- so you have launch range over land. If there are roads up the mountain then you probably have people living around the area. There other things like being in a different country if you want to launch near the equator [this can have all kinds of legal problems].
But suppose you had a island with somewhere around a 10,000' mountain and most of launch range was water and there wasn't any people in the area [say in 5 mile radius] nor were there animals or plants which are classified endangered or highly liked because they are fuzzy or something. Perhaps, the Island was US territory or some country which would work with US laws or work with whoever was launching the rockets. And you could buy or long term lease the land fairly cheap. There was a port facility somewhere near and had a road or a road could made fairly reasonably. If it had these things it could be a good idea. Having a launch pad at 10,000 would mean higher efficiency from the rocket because there was less atmosphere.

Now as to the added speed to rocket from pipelauncher. Let's say it's doing 1/2 gee for 10 seconds [112 mph] for rocket that can launch at 1/2 gee. So in simple terms it is saving the fuel the rocket would burn in 10 seconds. So you could simply not add that fuel. Because rocket weighed less it would be slightly more efficient, but other that it would be the same.

Another thing America has been launching rockets from 28 inclination for payload destinations a GEO stationary orbit, for decades and I wouldn't too surprised if Lockheed is still launching from 28 inclination. Launching from higher than the equator to get to GEO has a considerable delta-v cost. Russia at it's 51 inclination has even done this [which has a really horrible delta-v cost].
So my point is that governments aren't very concerned about doing anything which is efficient.
The EU which involves the private sector in it's space program is launching from 7 inclination. Sea Launch which completely private is launching from equator.
The equator is simply the best place to launch a rocket- unless you want to have a retro-orbit or with polar orbit it's not much an advantage. In other words forget about a mountain- having a launch pad at 100' elevation at the equator is far better location than every government launch site currently in the world.