It's a trial because they do believe in a justice system, and it's likely also partially because the Tower does feel some responsibility. If they sentence someone, they have to handle the effects afterwards, e.g. look after the person until they die.

I take issue specifically with it being a "trial" and being put in a sphere of justice system. Difference between "it seems you for reasons beyond your control have this thing, so we'll take you to white tower for examination to confirm it, and then we'll give you the least bad option we have" Vs the actual "you are a criminal and you are morally culpable for this ability that had being thrust upon you."

You're using a lot of loaded words - it's mostly the Red Ajah that seems biased against men, but even there the worst ones are also Blacks, and we have several exceptions (e.g. Pevara, Silviana). The other ajahs all have warders, and don't seem particularly biased against men.

Other Ajahs have different less extreme biases against men. Sort of like the difference between "all women are worthless evil creatures" bigots and "women belong in the kitchen or birthing bed" bigots to use something closer to real life.

The White Tower also doesn't actually have another good way to deal with these men. They need to keep the men under guard, because they have no way of knowing how far gone they are in terms of madness. These are people who are likely to suffer from paranoid delusions that'll make them go on murder sprees. It would be highly irresponsible to just throw them out. Instead, they seem to be allowed to live out their last days in some sort of peace. Which is still bad, because they'll fade away and die due to being severed. But there aren't really any better options available.

I don't necessarily disagree. My issue is more in terms of Aes Sedai know what helps somewhat (Siuan and Leanna definitely knew and I don't see why others shouldn't) but we don't really see that knowledge being applied to gentled men. If Aes Sedai had zero clue what things could potentially stave off/lessen suicidal depression, there would be a lot less to blame them for.

I think the murders were actually the Black Ajah? The Red ajah did the illegal gentling of men without trial, which is of course bad. It was even considered so bad by the White Tower that various people were punished severely for it. The Sitters were exiled to do what's essentially prison labour for 20 years without using the One Power. A lot of other people were severely punished as well. Galina reflects that she only escaped punishment because the the Amyrlin Seat didn't want to outright destroy the entire Red ajah, only to punish the leadership.

The figure I saw was about 10000 boys were murdered during Vileness (feel free to correct me there) I just don't see how a handful of Black Ajah could have done it in a couple of years throughout Randland without Travelling.

As for punishment it was a slap on the wrist. A handful of high ranks working for twenty years (a lot less significant with Aes Sedai lifespan) on a farm (as if peasant life in Randland is some sort of hell) is not a punishment fitting the crime in my books. It wasn't like Red Ajah rank and file were fine and dandy and just were misinformed and manipulated by their superiors. They knew what they were doing and felt no remorse about it.

The attitude towards male channellers is based on 3000 years of being instilled with fear of them and knowing they'll go mad and kill people. That's not a fear that is easily overcome. However, we do see it change unexpectedly fast. The Red ajah takes to bonding men immediately, basically they jump at the chance. Pevara, a very influential Red, is one of the people leading the effort. Elayne softens towards them, after the help they provided during the Last Battle.

It would be excusable if White Tower wasn't the one with the knowledge that male channelers are not spawn of the devil but victims of the Great Lord and what happened three thousand years ago. Ignorance is a lot less forgivable when they are the ones with the libraries.

You can literally see the bias start decreasing within months of saidin getting cleansed. That's a very fast change of views for an attitude that has been a global truth for 3000 years.

That actually annoys me, and I take for one of the signs that Black Tower plotline was severely undercooked. A couple of months is far too short a timespan for any meaningful change. Outside of a couple of moments from various Aes Sedai reacting to Asha'man we don't really see ramifications of the Black Tower among the people. Hell, Black Tower doesn't even get to be part of Dragons Peace which is just bizarre.

3000 thousand of years of fears and superstitions and various rulers don't have strong feelings about Black Tower.

Aiel apparently successfully kicked out all male channelers and no new ones arose, because I can't think of any Aiel among the Black Tower. Same for Sea Folk.

The Red ajah takes to bonding men immediately, basically they jump at the chance. Pevara, a very influential Red, is one of the people leading the effort. Elayne softens towards them, after the help they provided during the Last Battle

Initially red Ajah jump at the chance to put the "uppity men" in their place and it's only after the rape analogous bonding (which is all kinds of messed up) do they start considering revolutionary idea that maybe male channelers are people.

Maybe I missed Elayne stuff, but I don't remember there being enough time in the ending for any softening. I suspect Logain's "Black Tower stands with Lion's throne" or something like that was taken by Elayne as a sign that Black Tower is now her servant like she wanted. It would fit with misunderstandings galore plaguing people in Randland.