This is very true. In all peer reviews I've sat through, you can see these two types pop up again and again. The deft presenter will play the counter-type argument (and including with bounds to allow switching between the two viewepoints):
"There's no mathematical rigor" --> "That's a strength, it's simple, performant, and therefore easy to verify for our use cases"
"This is unnecessarily complex, and anyway you've ignored the constants. Our N is small." --> "Asymptotic performance just let's us sleep at night knowing it'll never be that bad. Here's a plot of the predicted and actual cost over our sized N's, you can see they agree well".
Perhaps the moral of the story is, be an engineer for your use cases, and a theorist for scaling.
"There's no mathematical rigor" --> "That's a strength, it's simple, performant, and therefore easy to verify for our use cases"
"This is unnecessarily complex, and anyway you've ignored the constants. Our N is small." --> "Asymptotic performance just let's us sleep at night knowing it'll never be that bad. Here's a plot of the predicted and actual cost over our sized N's, you can see they agree well".
Perhaps the moral of the story is, be an engineer for your use cases, and a theorist for scaling.