Biochemical experiments tend to contain compelx mixtures of molecules with a bewildering array of chemical properties. However, even in pure chemical solutions you would never reach 100% ionization of H+ in a solution, not even in superacids. You get close with superacids, but never 100%. H has to be seperated from an anion to be present in ionized form. But all anions (including the OH- cation that is left when H+ is removed from a water molecule) can attract cations including H+. What we have is a tug of war between all anions and all cations in the solution and an equilibrium will be reached depending on the relative strength of the pull of each.

Many biological molecules and preparations can act as buffers, minimising fluctuations in levels of H+ in the solution.