I worry my child relies on watching videos when we're out. How should we handle it?

For many families a video is a lifeline for waiting and staying calm while out, and that isn't bad in itself. First look at what role the video plays (relieving boredom, anxiety, or regulating stimulation), and make that role fillable by other means too. For example: decide on a short set time, carry quiet alternatives (picture books, sticker books, hand games), and show how long the wait is with a picture or timer. Rather than zero, "decide the situations and length and use it well" is realistic. When securing safety during travel comes first, there's no need to force it away.