The purpose of digital proofing is to simulate the color of the press, that includes overprint trapping and the paper color. Some software offers a 1 bit tiff others does not. some can simulate halftone dots ans some are integrated with their own workflow or stand alone.
This is also to predict or confirm the contecnt of the plate if your using 1 bit tiff it is true, if there are missing in the plate then then your CTP RIP software is not singing the same tune with your proofing software.
I can not create ICC profiles for your press to be used for his display and proofing system with just having color bars with solids and 50 \% screen of the primaries.
I do not know of any software with a maximum of 8 patches that create ICC profiles.
The inkjet printer is one of the most stable and consistent printer - so plese do not put to blame the inkjet printer if you can not get the right color in your press especially if you are not even using a densitometer.