I agree with your statements as written. However:

However, what is not morally coherent, is that women have sole power over reproductive decisions, but men have an obligation to support those choices whatever they may be, that husbands don't have a say, that unmarried men can be forced to support babies, but women cannot.

This is not nonsense, as far as I can tell.

Given "Accidental Pregnancy", the woman's decision tree (A) goes:

A1 - Keep the baby, support it, including whatever costs and benefits.
A2 - Get an abortion, costs and benefits are avoided.

The man's decision tree (B), according to the quoted statement, goes:

A1 - The woman kept the baby; (Bx|A1) - Support the woman and baby. What this man thinks or wants or would have decided is irrelevant.
A2 - The woman got an abortion; (Bx|A2) - No baby, no costs, no benefits. What this man thinks or wants or would have decided is irrelevant.

Once you've boiled down the calculations, given unforeseen pregnancy, the men have zero decision power according to such a system in theory, and must pay a cost independently of whatever they could possibly do in exactly half of the possible outcomes.

In other words, whether you pay a cost or not is entirely not up to you, for no specific reason whatsoever other than "aren't the ones using their bodies as life support". Does this sound like a fair setting, and more importantly, does it sound like an optimal system to play in?