Jennifer Hanna would be a dream hire for the many companies wrestling with talent shortages these days. Having worked in factories since 1991, she is responsible for more than 1,000 people building KitchenAid stand mixers that sit on countertops around the world.

Ms. Hanna, though, has worked for KitchenAid’s owner Whirlpool Corp. since she was a high-school graduate figuring how to pay for college. It would be hard to lure her away.

The...