But take a brand like Nike as an example. I can imagine Nike paying to put (one!) swoosh on an article on a site like ESPN. But Nike, if they’re doing their job right, would not want a swoosh to interrupt the reader’s experience — that’s the opposite of good branding.

Consider FM radio as another example. Ads on most music stations are obnoxious. Sponsorships on NPR are generally much more subdued, take less time, and don’t try to stand out.

(Oddly, NPR is quite obnoxious about their own fundraising placements. I wonder whether they would be more effective if they backed off a bit.)

Variations on "take-over" exist where you may have a "branded slate" in which the normal framing and background of the site will also be updated to align (and sometimes synchronize) with the "take-over" ads for that day.

You have likely visited imdb.com at some point in time. With so many TV shows and movies premiering throughout the year, IMDB has a higher frequency of "take-overs" than an average site.

The "pop-ups" or interstitials did decrease due to being bad design & bad consumer experience, but have returned and are now overrun with publisher sign-in and privacy/consent interstitials.