It IS important, because it affects the nature of the prayer, because it affects the mental inclination of those performing it.
Same thing with kneeling, genuflecting, etc. As C.S. Lewis said, we are souls, but we have bodies, and our physical situation (including our posture) does affect our souls.
I say the Our Father several times per day and on the few occasions when Mr. M goes to Mass with me I rejoice that I can pray while holding his hand. We also kiss afterwards which I am sure is not in the Roman Missal.