The government also wants stable couples (divorce are costly to society) and non-toxic relationship (because these too are costly), which is also what the users desire.
Maybe they should have a Rebound app as well.
The societal costs otherwise aren't just the obvious direct costs - there are other things like (in divorces where there are children involved) negative effects on labour force mobility.
There are many situations for which a divorce is better than staying in a bad mariage, but divorce are still obviously costly for society: it drives the housing demand up, the legal process is costly and encumbers courts, single-mom households are more prone to poverty and its negative effects, etc.
The key point is that ideal for individuals (a couple that is happy together) is also the ideal for governments.