Dear Subbudu sir, as you rightly observe, this samskara is an absolute must for all SVs, so much so, in orthodox families, a new DIL will not be allowed to touch anything in the kitchen, why, they may not even be allowed to enter the kitchen, until she is branded

.
Boys get branded when the get their second life - upanayanam, though many weekend SVs have no idea about this and don't do it, and the girls get branded when they get their second life - wedding. The one who performs this samskara becomes one's acharya, and therefore girls normally are made to wait until they get married so that the entire family will have the same acharya.
To be fair, this samskara is not only about branding with Shangu and Chakra, but it has five aspects to it -- for this reason this is also called pancha samskara. These five are:
- tApa samskaram, i.e. the branding part,
- pundara samskara, the acharya will place the urdva pundaram (namam) in twelve places in the upper torso, and one is supposed to wear this 12 pundaram from that day forward,
- nAma samskaram - all SVs take the same name, ramanuja dasan,
- mantra samskaram, the acharya will initiate the aspirant with three esoteric mantras that are of prime importance for all SVs, and they are, (a) thiruvashtaksharam, (b) dvayam, and (c) Srimat BG sharama shlokam; BTW, the first two are so esoteric that they must not be said aloud, and yet, even in the most important temple for all SVs, namely Sri Rangam, these mantras are broadcast on loud speakers -- so much for following tradition
, and finally,
- Ijjai samskaram, this is when you get the right to perform aradhanam to saligrama perumal, and all SVs are supposed to do saligrama aradhanam everyday and consume only what is offered to this perumal, this is the reason for all the exclusivity.
This panca samskara is not restricted only to dwajas, anyone can get it done, even a dalit. If the the stories of SV Acharyas can be believed, then we know that Dalits were indeed part of the SV community once upon a time. Even today, if somebody approaches a SV acharya and requests Panca samskara to be administered, they will do it, they have to do it, for, according to SV, each and every human is entitled to it -- வைகுந்தம் புகுவது மண்ணவர் விதியே, says Nammazhvar. These days, how they get treated afterwards is another story.
Cheers!