As said, most probably Christian heritage. Even in secular countries like France it is forbidden.
To be precise about France, only polygamous weddings are forbidden but being polygamous without being wedded is not illegal. I think it has historically something to do with central Africa immigration from the former colonies.
You could migrate to France and ask for family reunion to have your wife and kids legally come, but I guess they wanted to put some limits so it was decided that wedding means one partner only. Those laws were made by old right wing parties so it is kind of logical that they wanted to limit African immigration to 2 adults + kids instead of 4 adults + kids.
Would it be frowned upon? Maybe, mostly by older folks and more traditional peoples but the larger part of the population would just not care. The problem is with legal status, without a wedding you can have child care and heritage problems in case of death.
I agree with you, but:
Who are the other 10?