I tried my best to ask SciFinder, Google, and Google Scholar the wrong questions ...
I found many paper on the fitting of the solubility to some equations to be able to calculate the amount of $\ce{CO}$ in water, but I could hardly find any explanation on the low solubility. Only one paper [1] dealt with it.
Why is $\ce{CO}$ way less soluble in water than $\ce{CO2}$, despite, e.g., the first having a dipole moment and the latter doesn't? What am I missing?
[1] H. Sato, N. Matubayasi, M. Nakahara, F. Hirata, "Which carbon oxide is more soluble? Ab initio study on carbon monoxide and dioxide in aqueous solution," Chemical Physics Letters 2000, 323(3-4), 257–262 (https://doi.org/10.1016/S0009-2614(00)00508-X).