"Extensions" has just turned out to be a sub-optimal moniker. They're not some third-party-compiler-plugins-to-be-installed-into-GHC, they're more like (rather involved) syntax sugars you can enable if needed. Each such "language feature" amounts to a tiny sub-compiler necessitating additional "core-to-core" and "core lint" (Core being the intermediate Typed Lambda Calculus representation all Haskell syntax sugars, built-in or "extension", compile down to) passes during compilation, which in GHC feels pretty sluggish to begin with.

So in pragmatic terms, enabling/disabling "extensions" lets you prevent some unnecessary processing loads during compilation.

Obviously one can do everything in "vanilla" (no-"extensions") Haskell just like one could express everything in raw Lambda Calculus. Syntax sugars as always allow for reducing patterns of verbosity --- those provided by "extensions" tend to be such patterns-of-verbosity that don't always occur in-all-projects-all-the-time, just in enough-projects-much-of-the-time.

Most of the aversion to them seems kneejerk "but my other language had another (or none at all) approach to this" --- never understood the strong opinions about GHC extensions. "Other-language" typically also delights in a culture of repetetively verbose syntax itself and no such APIs to hack new language constructs into the compiler in a plug-and-play manner (without forking).

And yes one can enable these via cabal file or GHC -X flags, but there's something to be said for per-module pragmas: they only activate where needed, and it aids the code reader as to what non-vanilla syntactic constructs are used in the-module-at-hand.