No, they won't because they think amps are magic. They aren't, they just power the headphones. The LCD-X doesn't need much power. It'll sound just as good out of a smartphone as a $500 amp, as long as that smartphone will do 0.8 Vrms into 20 ohms (or however much is needed for enough volume, probably less).
Meanwhile, IMO a $300 Grado will sound a lot like a $70 Grado with bowl pads
While they aren't magic, things like noise floor and power matter.
Most headphones won't sound their best connected to a smartphone because you'll hear that noise, and they don't have the power to drive them well.
As an example, I have headphones which have to be driven at about 40/100 if I connect them directly to my TV for a reasonable volume level. After about 50 volume, when you increase the volume any further, the headphones stop getting any louder. Connect them to a proper headphone amp and they sound a lot better than when they are connected to the TV at any volume. (level-matched)
I do agree that you should not have to spend huge amounts of money on an amp, but it does not mean that an amp is worthless.
I agree about Grado though. It's not worth buying anything over the SR-60 or 80 in my opinion, unless you can get a pair of HF-2. Those are the best of the John Grados in my opinion.