Welcoming those in attendance has become a particular sort of alternative or additional opening to the liturgy. I have written elsewhere about the importance of opening liturgically and theologically, rather with banalities or information focussed exclusively on the community itself, and those comments apply here as well.
There is a particular problem or pitfall with welcomes, however. Not that it is unimportant either that visitors are received warmly, or that the character of God’s gracious hospitality is communicated.
I have come to wonder, however, whether there is an inverse relationship, in Anglican congregations of liturgical and sacramental character, between the likelihood of a pained welcome to visitors by the presider and the likelihood of there actually being any visitors. Welcoming people has often become a shibboleth of inclusiveness for congregations which are not really lively enough to attract or keep newcomers.
To get to the heart of the matter, though: Percy suggests that it is not appropriate for a minister or presider normally to welcome the (other) members of the community to the celebration of the Eucharist. This would be to suggest that the minister(s) are themselves the hosts, and the other participants guests. Doubtless such welcomes are well-intended; but the message conveyed is less hospitable than clericalist. The Eucharist does not belong to the ordained, but to the baptized; the baptized do not need to be welcomed by clergy to what God has already made their own.
Some may object that the clergy—or at least a presiding priest—may be acting in such a way as to represent and communicate God’s continued gracious and open welcome. Percy does not dismiss this idea, or the notion of "priesthood" that it implies, i.e., that the ordained may have the particular calling and charism in the liturgy of representing God and people to one another. However these elements of priesthood are secondary to the more fundamental and biblical sense that the people themselves are a holy priesthood; it is for them to welcome newcomers, seekers and so forth. The ordained priest does so too, but on their behalf.
This does not mean there is no room for expressing warm greeting, or "welcome" to one another in the mutual rather than hierarchical sense being addressed here. And the presider can offer words that express this mutual welcome and the joy of being present. How about:
"The Lord be with you"?