Hi, the title and the tagline can be supressed within the weaver options. But supression means, that the html-lines are only suppressed by css width class=hidden. The better way for google and less code would be, that this infos does not have an output in html, if supressed. (see lines 174 and 188 in header.php, Version 3.1.)
Your assumption of no output at all is not correct. We have very intentionally and carefully coded that to hide them with CSS precisely because it is absolutely essential to have that information there for Google and other SEO. It is very important. That is also why it is important to always provide a value for those fields in the WordPress Site Identity options menu instead of leaving them blank.
This approach has been carefully considered and discussed in great detail over the years by WordPress. In fact, there was a major change to the WordPress Theme API a few versions ago to be sure the site title and tagline HTML was properly handled and formatted to work best for SEO.