On a friend’s facebook feed, I noted a link this op-ed from last month’s edition of US Catholic.
I confess I don’t get trussed up about people arriving late for Mass. I commented on the link that (I think) I experienced a Spanish-language lecture at the beginning of the homily this past weekend. I caught some words about the purpose of Mass, respect, and the 4PM hour. Words were also delivered a bit louder than usual.
People have good and bad reasons for being late for Mass. My sense is that people come for something that has value for them. When people leave early, there’s something better to do than stay for minimal quiet time, repetitive and needless announcements, or a blessing that pales in comparison to the reception of the Eucharist.
With the beginning of Mass, if people are consistently late, I’d ask if the parish was offering any significant reason to arrive early. Does the priest hide in the sacristy till start time? Is there any sense of welcoming? Are there facilities for young children? Poor music? That extra homily before the Penitential Rite?
One comment in the article struck me:
I also arrived to pastor a parish at which the ushers used their arms and bodies to bar people from entering during the readings. (For some reason, you could enter during the responsorial psalm because it was “a song” I guess.)
It’s also the proclamation of Sacred Scripture.
Let’s get to the purple chair. Be seated and render judgment on how, if at all, you would seat newcomers at Mass.
Catholic Sensibility 
The line that struck you also struck me: I’ve never witnessed that, and it definitely reeks of concert hall performance practice. (Symphony Hall in Boston is so lucidly designed that you can see when the ushers quietly open all the entrance doors at the first (deliberate) pause in concert action to allow the seating of late arrivals.)
I wouldn’t do much about “handling” late arrivals. Particular cases might call for discerning particular addressing *outside* of Mass – as with everything.
Without getting into the monochronic vs polychronic culture debate and implications for a US church largely established by people who valued punctuality as a form of social consideration for others but that is now welcoming people from other cultures that may not (but still often do) have the same sensibility…I will definitely note that celebrants who become known for delaying what would have been a relatively prompt commencement of Mass incentivize further delay by latecomers, and feed the cycle accordingly.
I have a very strong bias towards arriving at least a half hour before Mass begins – because then I know that, in the places I tend to worship, I am much more likely to have at least a quarter hour to pray and reflect with reduced distraction. Getting to Mass just “in time” leaves me feeling flustered and out of sorts before I can settle into participation in worship. Then again, I come from a family whose culture was “if you’re just on time, you’re already late” and most of my circle of friends share some aspect of that to greater or lesser degrees – it’s a long-standing observation of mine that one of the biggest sorters of social circles in mature adulthood (after marriage and begetting of children) appears to be between punctual and non-punctual people (and it’s often a strain when the two types marry/partner).
And celebrants who routinely joke about their penchant for mismanaging ritual time only manage to rub it in congregants’ faces. If you know you have a problem, joking publicly about it does NOT give you permission to indulge it further – rather, it’s a show of clericalism.