And you can absolutely get this at home, but you need a proper machine. (A Moka pot won't do it. People might LIKE Moka coffee -- lots do! -- but it's not the same thing.) I'd rather pull a shot from my Rocket than go to any shop in town. And, as I said, I've had shots just as good from machines much cheaper than my R58 (like the aforementioned Silvia).
IME, genuinely good espresso is a fairly rare thing. The set of coffeeshops that pull consistently good shots is a much, much smaller subset of [Coffeeshops] than we might expect.
What an aeropress produces is more akin to French press than anything else I've had. It's absolutely nothing like espresso. Since I'm not a French press fan, I end up not caring for it, but that's a preference thing, not an indictment of the method. When it comes to filter coffee (which is to say, non-espresso), I prefer Chemex.
Given the notoriously grainy mouth feel of aeropress coffee, and the sheer joy I've had out of proper espresso made with even less-expensive home machines (e.g. a Rancillo Silvia, to say nothing of nicer home machines like Rockets), I'm utterly stunned by the weirdness of this assertion.
I wouldn't be more puzzled if you'd said the best you can do at home is a Mr Coffee. Dead serious.