From a social perspective, the point isn't that no one can tell you have a cyberlimb, the point is that you are making an effort to make it look normal and blend in. In 2075 cyber is everywhere, but the average Joe on the street will have synthetic because obvious chrome is predominantly associated with Shadowrunners, gangers, Urban Brawlers, and other antisocial, criminal types.
The media is largely responsible. Action trids are as close as the average citizen ever gets to the shadows, and the cliche of the chomed-up street sam or gilette has become ingrained into the popular psyche in 2070.
In our own timeline, there are lots of things that used to be common but have become unpopular with the general population because of their association with a particular criminal or counterculture subgroup. Black trench coats, Hitler mustaches, leather pants, bandannas (especially red or blue), double-breasted suits, thick black glasses frames; all have taken on specific associations over time that have caused them to be less popular in general. This in turn feeds back and makes them even more popular with the groups who do wear them and posers/fans/groupies because it becomes "theirs".
Basically, obvious chrome identifies you as a person who values the functionality of their cyber more than they value fitting into society. It doesn't mean you are a criminal, you could be a soldier, a bodyguard, a cop, or even a sports star. That's why an across-the-board social modifier doesn't exist.
The Street Sam infiltrating an Urban Brawl league event wouldn't raise any eyebrows with his 5.9 essence worth of gleaming chrome, and might even get a social benefit, but he'd better have a pretty good story to tell if he wants to attend a fancy ball, and either way he stands out, and people are going to remember him.
The face's synthetic arm wouldn't raise any eyebrows at even the fanciest parties because she is making a socially acceptable attempt to hide it. It doesn't stand out as unusual and the socially acceptable response is to ignore it if you even notice it.
To put it another way, a synthetic limb is a prosthetic first and a toolbox/weapon second. An obvious limb reverses that priority in a way that is very visible.