That has always been the case with musicals and opera - Not good to ask too many questions as the plot doesn't hold much water. Yesterday I saw a funny youtube video on some of the very convenient happenings in Les Mis. They mostly revolved around the fact that Marius and Cosett/Jean Valjean have hardly even met, let alone spent a day down the pub together and here they all are shouting about their undying love and hopes for each other.
It's like Mimi dying of consumption (a lung disease) in "La Boheme" and then spends a whole Act doing that singing her head off.
Or the fact that the lead role in Madam Butterfly is supposed to be a pretty petite little thing and yet is always played by a big battleaxe of a woman as that is what is needed to sing the demanding part.
All must be taken with a pinch of salt and just enjoyed instead of analysed too much.
The Cosette problem is only there in most stage/film incarnations because its played that a passive, inexperienced, but beautiful and genteel Cosette, and a manly, pretty, but gentle Marius is just what each wants - and its therefore love at first sight. It can just work if they can play the first look scene right. Its far stronger with a more assertive Cosette out to move on and get her man - but only one recent stage Cosette has been able to play that.
There's nothing wrong with the characterisation in Les MIs. It depends on what the cast and direction is like. The best casts fill in the details even where nothing is written so you will even see how everyone on the barricade relates to Eponine or Gavroche being shot. Many people don't see the detail because they are on a first viewing trying to keep up with the main story or they buy cheap tickets where you need a telescope to see the acting properly. It can be done though and good casts do it.