This question has been asked a lot of times, and I have repeatedly tried to clear the confusion here and there. So here is a sort of detailed answer.
TL;DR =
You are right, Nasr is ineffective against armored columns. The rationale behind developing Nasr is not that, but its about nuking enemy strongholds on Pakistani territory.
Tactical Nukes - the basic idea:
The idea that a tactical nuke would be used only against armor formations stems from the historical deployment of tactical nukes, e.g. by NATO against the USSR. One particularly famous example is the proposed usage of tactical nukes against a Soviet Blitzkrieg at the Fulda Gap in Germany. Fulda Gap is a natural bottleneck for such an armored column, so during the Cold-War, usage of tactical nukes against insufficiently protected tanks (of the cold-war era) would be highly effective.
Ineffectiveness of TNWs against modern MBTs:
You are absolutely correct in your analysis, that in the present age of NBC-protected MBTs, the effectiveness of tactical nuclear weapons against armor formations, in a flat-terrain region like the Indo-Pakistani border, is questionably low. Assuming a formation with vehicles 50-100 meters apart, a 1-5kt tactical nuke would take out only a dozen or two MBTs by the sheer explosion (inaccurate approximation, but you get the idea).
Cold Start - The reason why Pakistan developed Nasr:
Now common sense directs that the Pakistani military is also aware of the above stated ineffectiveness. So exactly what purpose does a tactical nuke serve in the Indo/Pak region? Why does Pakistan considers Nasr as a counter to the Indian Cold-Start doctrine?
To analyse that, you have to look up how India planned to implement cold-start. In response to a possible Pakistan-sponsored terrorist strike or any other similar event, the idea was to use small Integrated Battle Groups (consisting of MBTs, IFVs, APCs, Infantry & Gunships) to swiftly (in less than 48 hours) start crossing the international border at up to 8-10 locations, anywhere up to 50kms (I'm not sure about this figure) deep inside Pakistan, and HOLD those 'slices' of Pakistani territory.....BEFORE the international community steps in for the cease-fire because of the fear of nuclear exchange. These 'slices' would be later used for post-war negotiations.
In-short, Cold Start would have given India the ability to 'punish' Pakistan, without triggering a nuclear war. In detail:
Deterring Cold Start:
Naturally, this was a dangerous prospect for Pakistan. Cold Start essentially had presented India a loop-hole in the Pakistani nuclear doctrine, so that India could damage Pakistani forces AND humiliate Pakistan before the cease-fire without violating the official 'red' line and triggering a nuclear response.
In order to deter this threat, Pakistan had to find one or all of the following solutions:
1. Prevent Indian IBGs from advancing into Pakistani territory via conventional means.
2. Prevent Indian IBGs from advancing into Pakistani territory via nuclear means.
3. Defeat the Indian strongholds inside Pakistani territory & regain it before cease-fire via conventional means.
4. Defeat the Indian strongholds inside Pakistani territory & regain it before cease-fire via nuclear means.
Let's discuss the solutions:
1. Given the sheer qualitative and quantitative conventional strength of the Indian military, and the relative weakness of Pakistani military (no SADARM-type munitions as of yet) Solution 1 is difficult to implement. It is not impossible, but there is a chance that Pakistan would be unable to do so.
2. We've already established that in the modern age, Solution 2 is largely ineffective.
3. Solution 3 is much more difficult than Solution 1 because it will also take more time, taking us close to the cease-fire.
4. This leaves us with Solution 4. That is, if the Indian IBGs invade and hold Pakistani territory, the solution is to simply nuke the military elements (camps, headquarters etc) holding those areas, hence nullifying the entire point of Cold Start, and putting the ball back in India's court. The holding military elements cannot possibly be NBC protected for lengthened duration, most of the personnel and equipment have to be out in the open to operate a stronghold. Thus, Nasr plugs-in the loop-hole by being a low-cost and effective deterrent to Cold Start.
10 points to Gryffindor!
Why a 4-missile system? It's more efficient way to cover an area using multiple low-yield warheads.
Why not use, say, a nuclear Ghaznavi instead? It's not that surgical, it has a higher TEL signature and requires slow launch preparation routines. Nasr is more accurate, looks like a simple conventional MBRL launcher (or a truck if covered up), and is more robust (shoot-and-scoot).
Some may question that how could Pakistan nuke its own land? The answer is that firstly, Cold-Start is effective only in largely uninhabited areas. Areas with higher population density would instead slow down the invasions. Secondly, nuclear weapons when detonated as air-bursts leave minimal to no fallout, and also inflict the most damage via over-pressure. So nuking enemy forces inside your own territory (which is largely uninhabited) is not a bad idea at all.