They don't crash the computer. Sometimes there's no effect at all, the color looks right. This is especially true of large flat featureless areas. This is jarring and annoying when switching from one application to another. Today, the advantages to web designers of limiting their work to the 216 web-safe colors are not as strong as they once were.
Most computers can display millions of colors at a time.
And there have always been distinct disadvantages. Pastels and earth-tones are especially sparse in this set of colors. Many designers are throwing off the web-safe yoke for convenience or to more precisely realize the colors they envision. Antique computers remain in service that can only display 256 colors at a time. I saw a room full in a training center.