Even if one can make use of statues in prayer and liturgy*, could one pray with a statue depicting Christ or His saint smiling? (As opposed to making a pious gesture or a quick devotional prayer?) I don't think so.
"Does the Latin tradition have a problem with the use of images in prayer?"
*Can one use statues for the same amount of time as one can use two-dimensional images? I think because of their depth, the matter of the statues would eventually become distracting.