I kinda wish she would do a total surprise release of the "Do What U Want" video just to get it out of the way.
Like, imagine if she made an agreement that MTV exclusively (no VEVO, no Fuse, no Music Choice, no MuchMusic, etc.) can put the video on their MTVHits playlist (without putting it on their "Future Adds" bulletin) so the first time someone would see the video would be random.
Like, imagine you're just chilling, and you have MTVHits playing in the background, and all of a sudden, you hear the intro of the video playing. When the song starts, you tell everyone online that the "Do What U Want" video is airing on MTVHits, but no one believes you, until they put on MTVHits. Most people only catch the last 2 minutes or so, and frantically look online for the rest of it, but they can't find it bc it's not released to other outlets.
For the rest of the day, stans have their TVs set to MTVHits hoping to catch another re-airing of the video. Fans who don't have access to MTVHits have to deal with LQish recordings, but overall the hype and excitement goes through the roof. A week after this whole ordeal, the video is finally released to other social platforms in HQ, and stans rejoice.
...Actually, that would be a great hype tactic for a surprise lead single by any pop girl.

Imagine people saying "OH MY GOD THEY'RE PLAYING THIS NEW BEYONCÉ SONG AND MUSIC VIDEO ON MTV OMFG????" and people anticipating official iTunes/radio release of the song a week later.