This is very fair. I have a close male friend who was the victim of intense domestic violence, physical, emotional and financial manipulation by his ex partner.

He talks about how child support staff (like reception for example) are, are not favouring of him. They see DV in his profile and assume he's the perpetrator instantly. He had to explain himself constantly, no doubt reliving trauma when he does.

He has been struggling with the courts to gain sole custody of his child.

And to top it all off all the posters around these places are, like you say, about women reaching out against their abusive male partners. Which IS an issue and IS statistically more likely. But you make a very good point about these systems being able to help both.