Do you think a woman should propose to a man?

I think it should be equally acceptable for either partner to propose, irrespective of sex or gender.
At the very least it allows the couple a chance to discuss where their relationship is at and their dreams, fears and goals for their future.
The big thing about marriage is the choice to commit to monogamy until death - but it comes with a huge range of legal and social pros and cons.
The reality is that about 90% of men and women commit adultery (according to psychological research).
I would recommend each person maintains their own career and income,
never sharing a bank account, debts, credit cards, or the title of any property,
each pays equally towards the costs of raising kids,
and always signing a prenup with the help of a lawyer even if you never expect to become affluent.
Since living together for two years or more now creates the same legal status as marriage,
I'd recommend always keeping a separate place, even if letting it to a tenant or sub-tenant.