Trans bathroom bans are ultimately just a means of driving trans people from public life entirely.

This is not an exaggeration, the anti-trans movement literally aims to “eradicate [trans people] from public life entirely”, those are their words.

Here are some citations, numbers, and evidence to back up what you’re saying and why we should view trans bathroom bans as genocidal rather than about safety, like anti-trans activists claim:

When laws permit transgender people to access sex-segregated spaces in accordance with their gender identities, crime rates do not increase. There is no association between trans-inclusive policies and more crime. As one of us wrote in a recent paper, this is likely because, just like cisgender folks, “transgender people use locker rooms and restrooms to change clothes and go to the bathroom,” not for sexual gratification or predatory reasons.

Conversely, when trans people are forced by law to use sex-segregated spaces that align with the sex assigned to them at birth instead of their gender identity, two important facts should be noted.

First, no studies show that violent crime rates against cisgender women and girls in such spaces decrease. In other words, cisgender women and girls are no safer than they would be in the absence of anti-trans laws. Certainly, the possibility exists that a cisgender man might pose as a woman to go into certain spaces under false pretenses. But that same possibility remains regardless of whether transgender people are lawfully permitted in those spaces.

Second, trans people are significantly more likely to be victimized in sex-segregated spaces than are cisgender people. For instance, while incarcerated in facilities designated for men, trans women are nine to 13 times as likely to be sexually assaulted as the men with whom they are boarded.

…

In society at large, between 84% and 90% of all crimes of sexual violence are perpetrated by someone the victim knows, not a stranger lurking in the shadows – or the showers or restroom stalls. But trans and nonbinary people feel very unsafe in bathrooms and locker rooms, though others experience relative safety there. In fact, the largest study of its kind found that upward of 75% of trans men and 64% of trans women reported that they routinely avoid public restrooms to minimize their chances of being harassed or assaulted.

from: https://theconversation.com/baseless-anti-trans-claims-fuel-adoption-of-harmful-laws-two-criminologists-explain-206570

These laws aren’t designed to protect cis women, they are designed to police gender (this impacts cis people too!) and eliminate trans people from public life.