Amongst the people I know who swear with reasonable frequency, I don't see any correlation with lack of eloquence. Indeed, I can think without trying very hard think of published authors, professional screenwriters and famous Shakespearean actors who would fit into the "uses profanity reasonably casually" description.
But eloquence isn't binary; it lives on a gradient. Where there's a common, monosyllabic, four-letter word, it could be displacing another with a fair likelihood of being more interesting.
In fact, I'd argue your Shakespearean actors are far more likely to be making a compromise than an ineloquent person who'd otherwise drop the modifier or use a simplistic alternative.
So they're not rendered ineloquent as people, of course; but less eloquent than they'd be without that crutch.