No, the greater majority of monitors are at or around sRGB
Monitors can be either AdobeRGB or sRGB depending how the monitor is callibrated.
The monitor profile is quite different to sRGB (which is a colour space, not a device profile). In camera colour space has no bearing if he shoots in raw anyway.
The monitor profile is generated when the monitor is callibrated and used by the OS. The profile will be different depending on what color space is used - AdobeRGB or sRGB. In camera color space should be the same as the monitor color space. I'm unclear aboout your statement that in camera color space is unimportant because the OP is shooting in RAW.
Generally for pro-sumer printers, the canned profiles are pretty close when used with OEM papers. I tend to think the issue here is more of a ink age, print head issue
I agree.





