As I recall, one of the animated discussions my reservist kaki's
had during training downtime - plenty of time for them when out in
the field - was whether SAFPU could be considered an local elite
force, in the same mold as Commandos, Guards, Navy Diving Unit,
RSAF Black Knights, etc.
There wasn't a consensus. Obviously, many of its sub-units have
extrajuristical military powers - eg. MPs, SIB investigators,
anti-riot squad - & as such SAF soldiers, regardless of rank,
held them up with appropriate respect. But many of us also thought
that its precision-drill unit created a negative perception, in the
sense that the public thought that's all they do (beyond the
"discipline master" niche within army camps).
I also believe that, come reservist, a lot of them were
individually redeployed to become PDF troops, & thus "looked
down" upon by soldiers with frontline, ops-ready combat
outfits.
But, for BMT during my time, SAFPU was definately one of the
postings the better-performing recruits could aim for (besides OCS
& SAFINCO/SISPEC).