Valorant is very role dependent.

The agent you pick should determine how you play: if you play Jett by all means prime dash and be first onto site, however if you're Astra hopefully you're not going first onto site. The issue is that the current RR system promotes fighting and getting kills, which incidentally is more difficult for roles that require survival and more passive gameplay: ie all controllers.

If my Viper is swinging first every round and dying and leaves us with no smokes all round it makes winning a lot harder, so what happens? controller players rightfully play more passive because the util is important to the team. However what happens when you're passive? You don't get kills and the system determines you to not deserve as much RR and you also sink in the scoreboard.

Ask most controller players and they know when they pop o ff or match MVP its generally because their team sucked. A good controller ideally has less deaths: look at Pancada vs FURIA, he no doubt was crucial to winning and he went negative over 3 games (41K, 47D) but died the least in the lobby. If it were ranked, Pancada's RR would be terrible due to bottom fragging and going negative. That does not even consider encounter bonuses which are a whole other factor that promote getting kills over playing smart.

What changes (if any) should be done to reward better team behaviour instead of solely frags?

One way to start could be by rewarding clutches since sentinels/controllers often find themselves last alive. Also clutches don't currently reward a lot because a 1v2 clutch still get less combat score than 1 first blood.