Those the problems that I mentioned. Those problems are why you don't use pixels instead of `em` units.
If you increased the font size in a PDF then columns, diagrams, and layouts would also break. But you wouldn't be surprised because you don't expect the PDF to be responsive. We expect the browser to be responsive.
The use-case for font-only zooming in general is that as a designer, there are elements that should scale with the font and elements that shouldn't. Full-page scaling works by acting like the browser is just a lower resolution, so everything scales upwards except percentage units and viewport units, including things like border widths, spacing between columns, etc... Sometimes as a user that's what you want. Sometimes it's not.
As a designer, it's useful to be able to have more control in the scenario where a user wants to scale only the font and not the border-width of an element to make something that genuinely feels responsive, rather than to be completely subject to a zoom method that is just pretending you're on a screen half as large and then upscaling before it renders.
It's also useful because we'd like to build the web into an extensible platform that users can interact with in creative ways. So maybe we'd like the ability to scale only part of a webpage. Maybe we have an extension that allows us to quickly zoom in and out of a paragraph.
Note that this is not completely theoretical, Firefox already lets users set minimum font sizes. If I set a minimum font-size of 14px, it doesn't matter if you say that your font-size is 8px, it will render at 14px -- but all of your bigger titles and headers will be unaffected. That's the kind of feature that works if browsers allow font-based zooming, and pages are built to accommodate that, but that is impossible to do if the only way we can resize a page is with full-page zooming.