In Design Patterns in Dynamic Programming, Peter Norvig notes that strategies are just trivially replacable with higher-order functions (HOFs).
So that's where this trope is from! A few things:
1. The "just replace it with a higher order function" thing obviously falls apart when your strategy has multiple methods. In which case, the FP programmer might be tempted to supply a record where each field is a function, and maybe they want to close over some shared implementation details and... you've just re-invented objects, albeit memory in-efficient ones.
2. In many languages that support OO, a higher order function is an object, same way a string is, or an Integer.
I might be being harsh here. Presumably Norvig wrote this in the hey day of "OO flavoured" languages like C++ and Java being completely dominant in industry. But in 2022 we can stop repeating this tired trope.