Lower coefficient of friction in the boundary regime is a desirable trait in gasoline engines.
There are so many different types of FMs, so it is hard to generalize cons. Some will increase sulfated ash (those containing metal atoms like Mo) while many contain sulfur. Cat. converters don't appreciate either of those, but the engine itself generally does. They increase cost to the formulator which the bean counters don't appreciate.
PCMO vs. HDEO protection in a gasoline engine cannot be generalized based on presence or lack of FMs. Coefficient of friction in the boundary regime probably can be generalized (with expected outlyers and exceptions) between the two classes of oils on an equal viscosity basis: PCMO usually less coeff. of friction than HDEO.
As MolaKule's post in the linked thread says, the term is lubricity is "now considered obsolete".