Mamma Mia! The Nonsensical Movie

Just thinking the other day as I was driving down the road-as I am wont to do-and I thought on the popular film called "Mamma Mia! The Movie" From my recollection this film is about a girl who invites 3 men to her wedding, one of whom she believes may be her father (she doesn't know which one is her father). It was a very popular film making back over 10 times its budget (possibly due to songs by ABBA making up the majority of those used, particularly the title song Mamma Mia).
I had a major problem with the film as the premise of the movie is that the main character (Sophie, the girl getting married) wanted to know who her father was and yet the issue of a paternity test never arose. The possibility that a DNA test (which are 99.99% conclusive today) was never brought up or given a moments notice, but instead she invites the 3 guys over to her parents' villa to talk with them before the wedding in order to accomplish this. Okay...So the only possible explanation for this I could guess was that the film was set in a pre-DNA testing time. At this point I gave them the benefit of the doubt-at least until I did my research.
Research done, low and behold I discover that, although this film was produced in 2008 it was adapted from a 1999 Broadway musical of the same name. So, it was not originally created before say the 1980s (when DNA parental testing could be done with 99.99% accuracy). Of course Broadway musicals don't give much mention as to the setting-at least when it comes to exact year. The film from 2009, however, did make some mention of a year setting. That info found I also discovered that the setting for the film (though a date was never specified in the film) was probably in the late 1980s
due to there being mention of Sophie being a kid in the 1970s.
So neither the original adaptation nor the setting were pre-DNA paternity testing days.
My only conclusion therefore is that DNA was totally ignored as existing even though it would be able to identify without error who Sophie's father was-which was the whole premise of the movie. Why is science being ignored? I could maybe understand it if either the original adaptation or setting was from say the 1950s or earlier, I wouldn't object to that, but neither are. So I'm just at a loss for the logic here.
However, logic be damned, the movie was a big hit. I guess it matters not to people if something makes no sense as long as it looks and sounds great. I'm an ABBA fan myself (I like me some ABBA songs, which were used in abundance in the film). Hell, I liked the movie Muriel's Wedding in at least some small part due to ABBA's music in it as well, though the premise of the film made much more sense than Mamma Mia!
I guess that if they made more movies like Mamma Mia! the studios would be rolling in money, seeing as how people loved it so much.
Here's some ideas for other movies that don't make sense, but could make millions if put to music:
Yay! Here Come The Unicorns!
Moby Dick, The Resurrection
The Texas Chainsaw Highschool Musical
Rocky 8
You get the point.

There was one funny item of note I found while
doing my research on DNA paternity testing. This
was the fact that parental testing can be performed
easily through established companies in the US with
AABB accreditation (American Association of
Blood Banks). I thought it interesting the similarity
of ABBA (the rock group) to AABB. (Same letters,
just in a different order).