Paedocommunion

At "Theological word of the day" (one of my favorite sites) the word of the day is paedocommunion, which "describes the practice of allowing infants or small children to the Lord’s communion table."  As someone who personally sees infant baptism as something NOT in Scripture, I've long wondered why Presbyterians and Methodists don't also practice paedocommunion as well, or feeding the elements to babies as well.  It wouldn't be any different than infant sprinkling: the baby has no idea what's going on, has no understanding of the nature of sin, and basically an ordinance is incorrectly applied to someone who doesn't understand what's going on.  So why don't ALL churches that sprinkle babies also feed the communion bread to those "covenant babies" as well?  There's a pretty substantial inconsistency going on there.  As a reformed baptist, I believe that the table, and baptism, are ordinances that should NOT be observed by someone until they are at an age of maturity to understand the true meaning of what Christ established in these ordinances.  Anything else would be heretical.

I've wondered:  If a church practices paedocommunion, what happens with a parent that is exclusive breast-feeding a child?  Would they introduce foods like this when the child is only consuming the mother's milk?  Would they be forced to observe this as part of the "sacrament" of the church?