I don't think I have a perfect understanding of the topic, but an argument can be made that reiatsu absolutely needs a way to leave the body, somehow. Urahara plugged up Aizen's reiatsu vents, and he literally exploded because there was nowhere for his reiatsu to go. So, from that perspective, it's pretty clear that there's gotta be some way for their power to exit their body, otherwise they wouldn't be able to fight and they'd be blowing themselves up left and right.
At the same time though, even if other races did have "vents" like Shinigami do, that wouldn't necessarily mean that they're passively emitting reiatsu 24/7 whether they like it or not. Mayuri's statement to Aizen about the flow of reiatsu never stopping unless the heart is stopped is made in regards to Shinigami specifically. So, maybe that's the difference. Someone else can come along and correct me if I'm wrong, though please do, this has been bugging me for a while.