are those levels permanent or just for the day? they don't seem so according to serebii's website.
once you promote in rank, the average level of the trainer in the chateau improves as well. so for example, you start as a baron, and other barons will have lv15 pokemon. once you get promoted to viscount (which is pretty quickly), the trainers, now mostly viscounts, will have lv20 pokemon.
rank up enough times and you'll start spotting gym leaders and other trainers with high level. the writs are an aside that you can use to boost trainers' levels even more (thus getting the lv70-80 pokemon i mentioned).