I wish table headers did this automatically. If devs do the extra work to use <th> tags then this is likely the behavior they already want.
Unfortunately I'm seeing an increasing number of websites using 500 <div>s with 45 nested layers of <div>s within each <div> to create a table instead of <table>s so it wouldn't work on those.
why have everyone do extra work when one person could do it for everyone else in about the same amount of time that it would take one client to do?
Also, we already have a situation where different browsers have different defaults leading to an overall worse UX of the web.
So please, let's not do this.
I use tampermonkey, but I have it restricted to just one domain, which it complains about every time chrome is restarted.