The ISO 29621 Second edition 2017-03 provides some definitive answers on this issue. Quoting from this document:
“Alkaline pH may also create a hostile environment and may in some products be used as part of their preservative system. Liquid soaps with alkaline pH (pH 9,0 to pH 10,0) present an environment unfavourable for the growth of some microorganisms (see Reference [11]). Hair curl relaxers, due to their extreme pH (around 12), prevent the growth of virtually all microorganisms that would be likely to contaminate cosmetic products (see Reference [12]).
The reason for this is that the extreme pH, either acidic or alkaline, makes it necessary for microorganisms to expend energy on maintenance of intracellular pH rather than growth. When pH is used in combination with chelating agents, glycols, antioxidants, water activity and high surfactant levels, an environment can be created which will not support microbial growth.”
Works for us. Of course every new product we produce is Challenge Tested, and each batch manufactured is tested in our microbial lab before release.