Human blood is limited in availability, and would be phenomenally expensive as well as having the reproducibility problems you mentioned. We use FBS (fœtal bovine serum) as a substitute. It's routinely added to culture media such as MEM and DMEM; 10% v/v is typical. This is still pretty expensive though, as well as having ethical concerns (the extraction process is horrific).

It's also still rather unrealistic. Most cells aren't directly exposed to blood plasma and all of its proteins. They are perfused by interstitial fluid which is blood plasma filtered through the capillaries.

One of the goals of some of the more modern media (as in this article) is to supplement every known necessary component of blood plasma to avoid the need for any animal-derived sera, and to make the media completely defined and standardised. This isn't new; people were doing this over a decade back when I was working on my PhD. However, the number of components in blood plasma makes this difficult, if not intractable. Most of these new media had a small amount of FBS (≤1%) to make up for the unknown components. That notwithstanding, the efforts to better understand the exact requirements are laudable. However, proving that all the needed components are present and in the correct concentrations is difficult if not impossible, since it might appear to work while causing some subtle physiological change. We might have to settle for "appears to be good enough for all common cell types". But even that would be a huge improvement upon the status quo.