By activating “Avoid printed parts when travels”, won’t the printer head travel a lot more resulting in a way larger completion time for the piece?
Yes, activating the "Avoid printed parts" will increase the printing time, however, activating it will reduce the possibility that the nozzle crashes with the printed part.
Also, if you are printing TPU this setting is a great help because the TPU can bend when the hotend is traveling over it. It helps to reduce the stringing/oozing and other superficial defects.
If you're printing with two colors or materials with the parameter enabled, you will avoid color and material contamination.