So as not to draw undue attention to yourself? Not alarm people around you? To maintain a level of discretion? To not risk someone taking your firearm away from you by robbery? Out of sight, out of mind of the an armedcriminal.
That doesn't answer the question though; why would I prioritize total concealment higher than reliability or shoot-ability (hate that word)?
I can't have everything; I cannot carry a rifle or shotgun, I will not carry a .44 magnum, so I have to make compromises- agree?
So if I consider the handguns in my collection I have to choose one that I consider to be the best compromise of one that is (in approx. order)
- a gun that has proven itself reliable
- a gun that has the ergonomics that contribute to my ability to shoot accurately
- a caliber that is effective at performing the task
- comfortable to carry
- a gun that I can draw from a holster well and with repeatability
- has a capacity with which I am comfortable
- is concealable
How you rack-&-stack those priorities is a personal decision. I'm asking why the OP placed concealable as number one.
After a decade of carrying openly and poorly concealing, I have never encountered a single person that was 'alarmed'. Of the people that I know or read about, their actual experience is the same. So why would I want another person's alarm to be such a strong factor that I would compromise the higher priorities?
'Level of discretion' has no bearing on my decision because 'discretion' doesn't help my cause in a mugging; in fact one time it prevented a (an admittedly minor) mugging from happening to me.
Risk of having it taken? Same. It's too rare an occurrence at this time to allow it much sway. That can change of course, and if that were to become a concern on any given outing I can simply adjust my concealment. It may still be poorly concealed but as mentioned by me and others; few are that observant.
Out of sight out of mind? Hey, I watched a guy obviously intent on knocking me down for fun or robbery change his mind when he finally noticed a full sized 1911 on my right side (he approached from the left). That incident makes several points; they ain't looking, deterrence actually does work sometimes, and out of sight would have proven detrimental. You see, I could not have drawn a gun on a guy walking away from me after punching me to the ground and taking my wallet. The only real option would have been to follow him until he got tired of me and came in for the re-attack- not a situation I would ever endorse!
So the question remains: If concealment isn't required, why on earth would I prioritize it higher when choosing a carry gun?