As I think it can be agreed that this phenomenon happens in all jurisdictions, I wouldn't say that it is specific only to Greeks.
I think there is a larger issue here. Sadly, I think that people come late and leave early as a result of sheer boredom and disinterest. Those who are uneducated in their faith don't understand why they need to be present for the WHOLE liturgy, and they have been taught by example that this behavior is not only acceptable, but in some cases, expected. It comes down to this... IF THE DIVINE LITURGY AND COMMUNION WITH GOD WERE TRULY IMPORTANT TO THEM, THEY WOULD MAKE THE EFFORT TO BE THERE ON TIME.
I understand that it is difficult to get children anywhere on time and difficult to keep them interested and quiet (I have godchildren/nieces/nephews myself). However the most important place for those children to be is in the Liturgy, and the most important thing for them to learn is their faith. They won't learn this by being kept away for fear of making a disruption. Most priests are supportive of parents whose children make a little noise (one priest whom my family is very close with says that the children's' chirpings are their way of talking to God and His Saints and His angels). They should be allowed to participate the way they are able to, as we adults do.
As far as being late because of the children (this is one I hear often... from people in my own family), how do you get them to the doctor on time, or school, or to playdates, or anywhere else? I understand that lateness happens sometimes, but all the time?...
I think what it boils down to is that it just isn't important enough to them. We have to pray for them, and we have to do our best to minister to them as Christ would and bring them back to Him.
Hope I'm not offending anyone... it is definitely not my intent.