Smartest move by E. Jean Carroll's legal counsel:

[Liberal In Texas]

15. Many, not most. And not a majority.

It costs a bunch more money and one side usually has to pay for it. Generally the plaintiff side can't afford to set it although they usually do pay for a copy. Normally the defense side (usually the corporate side) requests video and the plaintiffs will buy copies to keep them on an even playing field. I would guess with this high caliber litigation both sides had a piece of the video costs.

And the video itself isn't the only cost usually involved. The attorneys will want to have it synced with the court reporters transcript. This makes searching in a 6 hour depo for one specific thing doable during a trial or just necessary to cut down on the amount of time doing prep. Playback during a trial has to have the specific clips ready to go without having to take an hour to search for them. Playback during a trial is usually done with computer programs like TrialDirector. There isn't much point in have a video deposition if you can't use it effectively. All of this adds to the cost for every step.

Legal support people like to pay the bills too.