My wife was telling me about how in Spain, it's common practice to just go up to receive communion pretty much at random whereas in my experience I've always filed up (even when I was in Germany for World Youth Day). So I'd imagine some Catholics file up and some go up at random. Buy what is the reason for filing up, or if that is indeed the more ancient practice (which I somehow doubt it is) what is the reason for going up willy nillly?
I can give you an answer based on my experience.
I live in Rome, I'm Catholic, and I have travelled quite a lot. Every time I travel I search a local catholic mass.
I can tell you with a 99% of certainty that this is a cultural matter, dependinding on the community.
Here in Rome people is more or less ordered and goes in line. In France they have a more complicated 'algorithm': the one who are in the last benches go first, then the line builds up bench by bench from the last to the first.
A convincing example is this one: I went to the masses for holy week in Amsterdam. That is to say 3 masses: Thursday, Friday, Sunday (Saturday there's no mass in the holy week). As Amsterdam is quite multi-cultural, once I went to the local (Dutch) community mass, once to the french speaking community mass, once to the Spanish community mass.
In the dutch version they went in a line starting from last bench. In the french-speaking, mostly were from Africa and went in a line which was randomly formed. In the spanish community mass, people was much more 'unordered' and they crowded in the direction of the priest giving Eucharist.
So, summarizing, It seems really to be a cultural matter.
Assuming "file up" means going row by row in an orderly manner vs. "random" meaning everyone gets up at once and fills the aisles...
I see both in the church I go to with my wife. For important dates, when the Cathedral is packed to overflowing, ushers go to the front of the church and slowly move to the back of the church indicating to each row in turn that they can go up. The rest of the time, when the church is far less crowded, people pretty much stand up, move into the aisles and line up there. People who get up a bit later have no problems cutting in or some people wait until the end of the line goes past them then join in.
By contrast, most times we've gone to mass while on vacation in the US, the more orderly routine with ushers predominates, even with fairly small numbers. I think it's just a matter of what works for each parish.