First, do not use regular paper on inkjets. The colors will render poorly and the ink will bleed. Inkjet paper has a special surface coating that causes the ink to instantly dry without soaking in. This also gives rich colors and deep blacks. Some printers have special settings for regular paper which limit the ink. Check the driver settings for that. But they will still do a poor job. Also, for printers that can print on regular paper such as the dye based printer you use, profiles are not provided for regular paper and you can't just choose another profile randomly. For any specific paper there is only one applicable profile and driver setting.

On to profiles.

While profiles that direct inking to CYMK printers can be made that reduce ink usage at the cost of gamut size, profiles that control device RGB values can't. Colors map to only one formulation of RGB triplets. CYMK profiles, which require special software called RIPs can be tuned to alter the proportions of the chroma inks CYM (Cyan, Yellow, and Magenta) against the black (K) such that less CYM is used in proportion to black. Standard printer drivers are RGB and there are no options to alter the mix for any given color. Some printer drivers let you alter and possibly reduce inking levels but doing this will require you to make a custom profile for each configuration and it would be difficult to tell how much benefit would accrue - if any - until you test it.

Different papers have different inking requirements with matte type papers typically requiring more ink per unit area. This is a property of the paper, not the profile in RGB based printers.