Is there an advantage to saving my Incubators for 5 and 10km eggs?

Seeing as incubators are limited/costly, should I save my Incubators for 5km and 10km eggs, and only use the free infinite one for 2km eggs? Or, am I better off using my Incubators as frequently as possible for a higher chance of 5-10km eggs?

My goal here is to maximize the value of my output (rarer pokemon/more candies), while minimizing (using as few incubators as possible) how much I have to spend on Incubators.

It's generally accepted that saving your limited-use incubators for longer distance eggs is preferred because you get more time of having multiple incubators. With this logic, you should probably never use a limited-use incubator on a 2km egg and never use your infinite-use incubator on a 10km egg (unless you are out of extra incubators).

That being said, it might be worth making an exception if your inventory is full of 10km or 2km eggs. You are unlikely to run into this situation though if you prioritize those eggs to hatch. More likely is you'll fill your bag with 5km eggs which are acceptable to be hatched by either type.