It would never dawn on you because you're happy with your neat, but artificial, denominational lines. Rather like some people are happy with neat racial lines: let white be white and black be black, there's no place for brown. Um, news for you: neither race nor religion falls within neat lines.
Proof? History. Religion is an epic of human creativity. Religions have always borrowed from one another and loaned to one another, at the same time they are slaughtering one another. Your precious Roman Catholic church (which I know very, very well) is something of a Salvation Army store of religion; it's recycled an awful lot in its time.
Many non-Catholic people--mostly, but probably not all, Christian in belief--simply don't consider those denominational lines to be that important. They value, sometimes on occasion, sometimes regularly, being at mass, saying the prayers, feeling part of a worship service at which they believe Jesus is present (but they simply don't want to deal with the neat, but highly artificial, theology of transubstantiation). They see faith as a living, participatory thing, and their instinct is to participate. (This desire is particularly poignant for non-Catholic relatives of Catholics getting married or buried, and for non-Catholic spouses or children of Catholics.)
I suppose if the church posted signs forbidding non-Catholics to take communion, they wouldn't--but, in that case, it would be because they probably wouldn't feel any desire to join in the worship of such an unwelcoming congregation. In fact, from the strict denominational viewpoint you inhabit, it would be perfectly logical for a Catholic church to post such signs. Why don't we see this? Because the church wants to have it both ways: come in, you're welcome, we love to have you, we hope to sign you up--but don't touch our sacred sacrament till we tell you to!
There are a million other ways to argue the point, but the bottom line is that the Catholic church (i.e., its careerist hierarchy) has proprietary institutional interests here which it wants to protect. (And Catholic laypersons like yourself go along with that, because, after all, you've paid your dues.) Perfectly good business instincts. But the alleged founder of Christianity seems, from the accounts we have, to have preached a rather less proprietary view of human community and its hope of the Kingdom of Heaven.