It's a circular argument, since the main reason men aren't taking time off work to devote to parenting is the absence of such a leave.
The reality is that if you provide the leave, everyone will use it. (I work for a company that provides one, though a rather short one).
Ideally, the law will be written such that it's not an either-or scenario, and both parents could take the leave consecutively should they choose to (e.g. eligibility for a 6-month leave starting within 6 months of becoming a new parent).
And this will make it much harder for companies to discriminate, as it spreads the risks out. Old men can (and do) father children too.
This is not true. Germany introduced paid paternity leave, and the rates that men use it is still far lower than the rates of maternity leave usage. [1] Other countries might differ, Google wasn't providing me very good results for paternity vs maternity leave usage.