Hi Paul,
Am I correct or should the printer cover a wider colour gamut.
No, the printer will normally have the smallest gamut in the digital photo process.
See attached screen shot from a gamut viewer showing the simple 2D top view of various profiles compared to that of an Epson R2000 printer using Ilford Smooth Gloss paper.
The brighter gamut diagram is the printer profile.
1 You can see, compared to Adobe RGB, the printer has a smaller gamut
2 sRGB is roughly the same volume probably but does not match in some areas
3 My 600D camera raw is very much larger than the printer.
I have a fully profiled system and the results look to be a very good match to my monitor but that only covers sRGB
I would expect this as the aim of having a calibrated monitor and printer is to get the prints and monitor to match so you should be very pleased that is the case. The fact the gamuts are all different is part of what colour management sorts out for you.
Terry