Does the hardness (or other parameters of the water) not have an impact on nutrient or CO2 availability or uptake?
Not really. Some plants may prefer softer water, some fish/shrimp spawn better in softer water, but really you should try and work with the water you have as you can then concentrate on getting other things right, namely CO2 levels, flow and distribution.
My water is rock hard, 22' Clark (320ppm) and never had an issue with plants not growing and fish no reproducing like rabbits....
Some people sometimes, possibly, more likely falsely infer, that hard water prevents their magnesium and/or iron and/or phosphorus uptake by the plants, but I have not seen any issue.
People get all worried about the "Redfield ratio" (ratio of NO3 to P) being affected by hard water, but this has well and truly been debunked, both Redfield ration and any affect of NO3 and P uptake due to hard water.
Some people seem it infer that as water is hard therefore high pH there iron "unchelates" and falls out of solution and would recommend a better chelated iron that can survive high pH. Again I have not had any issues with my AquariumPlantfood micro's. (Solufeed B). The instructions for Solufeed B say, just mix with water.
As for CO2 injection, regardless of water hardness, a 1pH drop in pH levels equates to about 30ppm CO2. eg if your water is 4 kH and pH is 7.6 then dropping pH (via CO2) to 6.6pH will be due to 30ppm CO2, similarly for 20kH and pH 8.3 dropping to 7.3 pH will be due to 30ppm CO2. (OK I read these values from a table, but generally will be the same'ish in a tank).