"Imitation is the sincerest (form) of flattery."
- Colton
However pun aside, anybody can do anything.
Let me address a few of the issues being discussed on this thread.
Is the march on the double something that the SSG initiated? Not specifically. However, in the sub-continent, SSG were the first to put it on display during parades and eventually others, including the Indian Paras, adopted it.
The march on the double started in the 80s. Prior to that, SSG detachments, when and if part of the parade, would march just like the regular units. The march on the double was adopted to showcase the high fitness levels of the SSG and also as a measure of the "special" nature of the special operations troops.
Prior to the 80s, SSG did not take part in parades as they stayed away from the limelight. It was only when the then Commander SSG, Brig Tariq Mahmood, kicked this off. Prior to that, besides the maroon beret, SSG smock (worn ceremonially) and the commando wing, there was no other outward way of showing SSG troops differently than the regular troops. So for good or bad, SSG was showcased differently from other units by having them participate in parades with their smocks and the march on the double.
As to their cadence (chants etc.) while on the double, that too has changed over time. Initially it was just "Man Jaanbazum" in Persian (meaning "I am a jaanbaz") and then it became "Allah hu" with the Islamization brought into the Army by Zia. However to this day, the motto of the SSG remains "Man Jaanbazum" which I personally have always appreciated.
On the point about "Nara-e-Haidery", its a battle cry used along with Nara-e-takbeer. Leaving the theological aspects aside (i.e. using "Ya" with Ali RA's name instead of exclusively with Allah the almighty's name), both are still in use but the latter more so than the former.