Now, if someone were leafleting complete strangers with invitations to the Liturgy I'd agree with you, but I've certainly never seen, nor have I heard of, that or anything like it.
Yet we litter the internet with videos and photographs of the Divine Liturgy where they're available to any atheist, pagan, Jew, Muslim, and heretic. Even the faithful who attend the Liturgy, unable to peer behind the iconostasis, are generally not given to see what we shamelessly parade infront of any random individual who happens to stumble upon one of the thousands of videos that are up on youtube. One Russian priest I know referred to filming in the altar as "liturgical pornography", the exposure of the most intimate act of the Church, the Bride of Christ, with her Bridegroom.
Though you say that going back to the rigour of the ancient church is not desirable, why not restore the action of having all non-baptized members escorted out at the explanation of τας θυρας!? The Divine Liturgy is worship for only the Orthodox Christian. Those who are not prepared and not Orthodox shouldn't be there.
I agree, though now it's difficult to implement, at least in larger parishes, in a way that is pastorally sensitive and conducive to the salvation of those getting asked to leave (setting up an inquirers class or something might be a way to ensure people don't feel excluded.
However, as long as we don't even protect the holy Mysteries from the prying eyes of the masses on the internet, the expulsion of catechumens from the Liturgy seems a very secondary concern.
Good quote from Metropoitan JOHN, btw.
I forgot to include the page number, sorry - p.48.