When I was at a shooting range before, people were very cautious if you moved your gun awkwardly (even just vaguely pointing it in the wrong direction, like of a person, even with safety on, people wanna be 100 % safe with this stuff).
I think considering how unpredictable and messy SI can be, the potential window you would have to actually shoot yourself would be very small, and if you didn't do it asap, you put yourself at *very* high risk of getting hospitalized or arrested, which your SI might force you to submit to.
Or someone restrains you as soon as they can - remember, they don't know you, they don't know that you're only seeking to take out yourself and not a danger to others.
Better to have one in a private setting, if you can secure that?