This is a very accurate summation ime. I first came across it years ago when I use to criticize the trans lobby online on Twitter. A RadFem lady I knew on there said that as a man (apologies - I'm a male on Mumsnet but here and Kiwifarms feel like the last two places this is allowed to be debated so please forgive me my dangly bits), that as a man I could say things and not be attacked for it. I honestly thought that was paranoia at the time but realized soon after she was right. My criticisms were somewhat engaged with but often ignored. Whilst women saying the same thing would get both barrels. And this happened time after time.
I'm not a small fellow so I could see an element of that dissuading aggressive push back in real life, but even online just being male has shown a noticeable difference. I get the odd "burn in Hell, terf" dismissal but nothing like most women get. It genuinely triggers them that it's a woman pushing back, as you say.
I'd actually like to add one more reason to your list for the obsession with making women accept them. Female acceptance de-powers other men from acting. Probably sounds odd but most men want to protect women. Sometimes that may be white knighting true, but regardless if women asked for help because a guy had gone into their toilets and was perving on them, in any bar or club I'd reasonably expect a group of guys to quickly form and go in and remove him. But women are the gatekeepers of their spaces. When you think the women will side with the person harming them, it de-powers you from acting. It's a similar situation to when you see or suspect domestic abuse but know that if you do something, you're going to end up the one in the cell because she sided with her abuser (such is conditioned mindset of abuse victim). Transwomen seek the validation of women for all the reasons you say but also because it provides them a measure of protection. And that doesn't have to be physical like removing a guy physically from the women's toilets. It's social too as in this case. Matt Walsh makes a counterpoint to him and the guy hides behind saying "women say I'm a woman". Instant protection.
Transwomen will argue their case all day long but often what dissuades men from pushing back isn't the trans person themself but lack of social or verbal support from young women when to do so. Both women and men will to some extent patrol their own. Women more so than men but men also. But when a man appears to be "invited" by the otherside, that becomes difficult. Their no longer "your own", they've been taken under the wing and pushing back on them now means you're pushing back at an outgroup (women). Which isn't what most men want to do.
Anyway, I now realize having written all this, that there's probably no group that less needs to be told the value of speaking up more than the Mumsnet women's rights forums! : ) I've gone on a bit of a wander. But maybe this perspective might have some value.
But it's still the case that women - overwhelmingly young and at university or recent grads - reciting "transwomen are women" is a major source of male lack of support. I remember at school a girl reporting that a man had just exposed himself to her near the school. Immediately the entire rugby team sprinted off after him. Why? Because there was no ambiguity that women wanted us to take action.
It's why it really heartens me to see more and more women speaking out against the trans lobby. Because for all that Matt Walsh did a great job in this debate, what will really change things on the ground is more women speaking out and unambiguously rejecting "transwomen are women".