Delete ALL audio tracks

I was trying to do the same thing. Sadly, it's impossible to do in Premiere. There's always one audio track even if you delete everything. There's no way to adjust the Sequence settings to be only video sadly.

By @TorQueMoD2

There are several ways to work around this so it should not be a big problem.

In the top timeline below you can see how it looks when i grab a sequence in the Project panel. All Source patchings are lit up, A1/A2/A3. So if you drag the sequence now you will get video and audio. Since audio was something you did not want, just uncheck all Source patches so it looks the same way it does in the bottom timeline. If you now drag the sequence from the Project panel, only the video will be placed on the timeline. No audio will be placed in the timeline now.

So it is possible to drag a sequence from the Project panel and only bring the video part into a new sequence even if the sequence you drag has one or hundred audio tracks in it.

To uncheck all Source patches in one go, hold the Shift key down while clicking on either A1/A2/A3.

There are other workarounds as well.

That's not what they meant. They have a sequence with only an animation or video in it, and they want to be able to drag the sequence into another sequence for quick reuse. When you do that though, it also drags in an empty audio track which messes up the existing audio in your other sequence. There's also no way to preview a sequence because it's not considered a source so you can't drag only the video in.

It's really irritating, actually. I can definitively say the functionality doesn't exist sadly. It won't let you delete the last audio track and if you try to delete them from the sequence when you create it, you get an error that says you must have at least one audio track.
If there's no audio in a sequence, Premiere shouldn't try to insert a blank audio track as well. It's a total waste.