Thermal stability, as far as I know. So hyperthermophiles, presumably.

edit: hmmm. from this interesting review - https://www.sciencedirect.com/science/article/pii/S0959440X2... (open article) - it looks like some knots might increase mechanical stability and resitance to proteolysis

Oh, cool- they turned a not-truly-a-knot (open ends) protein into a truly knotted one (connected ends) and then unfolded it using urea and it stayed knotted. That's what you'd expect but it's also pretty cool.

It's interesting. That's the benefit.

Protein design is a multi-billion dollar field.

A single observation- thermostable proteases- was incorporated into modern laundry detergents, making Genentech and Corning billions of dollars in IP.

A category theory textbook opens the "motivation and use cases" section with the following poem:

There's a tiresome young man in Bayshore. / When his fiance cried 'I adore / the beautiful sea' / he replied 'I agree, / it's pretty, but what is it for?'