They are irrelevant, except for a few compounds that affect taste, if your local water treatment plant is doing its job properly. I've had the misfortune of renting in an area that did a half-ass job with water treatment, so I used those attachments as a precaution. The water did taste better, but hard water deposits were still about as bad as without it. Didn't run any tests beyond that though.

The issue really comes in with the lifespan of the filters. If you're intent on staying hydrated, you'll burn through cartridges (and $$$) like nobody's business and it's tempting to put off changing out filters for weeks at a time. And after several months, the attachment itself will leak quite profusely from the filter/passthrough toggle.

If you actually do need to treat your water, such as in the case of well water, and have access to your plumbing, it's much more economical to install an inline or whole-home filtration system.