The idea of color management is to characterize various devices with differing output characteristics by measuring what happens when specific colors are sent to those devices and create a profile for that device, then use the profile to transform the data to get what we expect rather than just what the numbers are (within the limitations of the device). sRGB is not an output profile. if your camera is creating an sRGB file, you want the color management system to transform those numbers through the monitor profile. Even if the monitor is an "sRGB" monitor you still want to create a profile for it, not use sRGB.
An sRGB monitor just means is the monitors gamut is large enough to show all the colors of sRGB ... but those colors won't line up perfectly.
As far as the printer if send a file to the printer and then let the printer manage colors, even if that image is sRGB, you have told the printer driver to manage the transform. so rather than managing it yourself, you've let the printer firmware designer do it. but it isn't being printed as "sRGB" ... it's being transformed by the printer driver.
You could send an sRGB file and have neither the OS, Photoshop, or the printer driver manage colors, but that would be a simple crap shoot ... most likely resulting in crap. It would be challenging to get any consistency.
But for best results, using the entire system correctly without trying to "shortcut" something because it seems to work is the best way to get some type of predictable results from screen to print. May want to check out
LuLa' Guide to Color Management ...