It reminds me of the recent Crowdstrike fiasco: apparently kernel level access was needed for their anti-malware to be able to properly work (because that way their net can cover the entire OS basically), but that high level of access meant that when CrowdStrike fucked up with an update, people's computers were useless. (Disclaimer, I am not a cybersecurity person and am not offering judgement either way on whether Crowdstrike's claim about kernel level access was bullshit or not)

In a similar way, in order for identity theft monitoring services to work, they surely will need to hold a heckton of data about you. This is fine if they can be trusted to hold that data securely, but otherwise... ¯\_ (ツ)_/¯

I share your unease, though I don't feel able to comment on the correctness of your mindset. Though I will say that on an individual level, keeping an eye on your credit reports in general (from the major credit agencies) will go a long way to helping there (rather than paying for serviced that give you a score and other fancy "features", you can request either free or v. low cost report which just has the important stuff you need to know.)

I also know that if you want to be extra cautious, you can manually freeze your credit so basically no new lines of credit can be opened in your name. This is most useful for people who have already been a victim of fraud, or they expect to be at risk (such as by shitty family, or a data breach). I don't know how one sets this up, but I know that if you did want to set up a new line of credit, you can call to unfreeze your credit, and then freeze it again when your application for the new credit is all done. I have a friend who has had this as their default for years now because of shitty family.