For realz! If only Minecraft Pets mod worked like this iRL (in Real Life), click on the mini animal pet to get them to stay put until clicked again (yes the wolf and others do that when befriended). Quite funny to see an army of little creatures chasing after Steve until they start getting in the way as you dig and accidently hit them. Stay!
P.S. Mob Pets is available in Minecraft Marketplace here.