Truth is that women have always had the privilege to know the child they had is theirs. Except in cases the baby was swapped, women always had the guarantee they are the parent of the baby.

If you observe carefully, technology is also an equalizer. War weapons have also equalized strength of men, so basically open-field combat is obsolete now. Machines made heavy work mostly made by machines, rendering the advantage of strength only marginal, which is positive for people who are weaker but also to prevent strong men and animals from being exploited. This shift is also what made women move further into the work force into jobs that made more sense when strength was a huge advantage, but since machines changed that, women can also work in those positions. In the same token, technology has provided women with tools of self-defense that are equalizers, which means a lot of women can defend themselves effectively using them, instead just relying only on authorities or men. Not to mention the huge advantage of smart phones and other communication tools, that make us way safer overall, in the sense we can call authorities or family as needed.

Technology, therefore, it is an equalizer.

Paternity test should be seen as an equalizer too, not as a tool to expose cheating women or shame them, although of course the consequence can be shame, the point is for men to have the same right most women have though history... to know they child they have is theirs.

Tests have also already evolved to detect conditions of all kind in babies, to quickly provide for them medical assistance and treatments. Tests are already standard, and paternity tests can just add this right to fathers to know the child they have is theirs 100%, and also for the children to know the parent they have is theirs and prevent later involuntary inbreeding with close biological family, have access to biological close father that can donate tissue, etc.

If the paternity test is standard practice, then there is no need for women to feel their partner is distrusting her. In the same token, most women also don't want their brothers or sons to raise kids that are not theirs and are products of adultery or cheating, so I think most women can agree with this from including the perspective of the men their love in their lives.

TLDR: I'm sure sometimes paternity tests are used to "scare" women, but truth is that the technology is a win win for men, women and children, just as other tests and medical advances, and also it is an extension of a right that women had but men didn't. Less resentful men, children knowing for sure who their father is, medical advantages of having access to close donators, more paternity rights, etc.