Safer seas with full rewards WOULD have an appreciable effect on the core game mode. But it would be a positive one.
The players who don't want to engage with PvP would just use safer seas, which means that all the players who WANT PvP would use the core mode. That means that when players fight in the core mode...they'd both engage in the combat! They might actually both ENJOY the combat! How wild would that be?
I've tried the combat multiple times. I enjoy ship-to-ship combat but absolutely have never enjoyed up close combat in this game. Not for lack of trying! But it's just not fun to me in the slightest. People will argue ceaselessly that since PvP is a core part of this game, if I don't enjoy it then 'Sea of Thieves isn't for you!'
But...the most fun I've had in this game has been playing on a crew with friends where for hours and hours we encounter nobody else. I CAN and DO have fun without PvP in this game! And plenty of others do too!
As it stands, whenever another ship starts to engage me in combat, I take one of 2 actions: Flee if I can, or Scuttle and Change Seas if I can't. I'm within my rights to do so since the game gives me those options; but when I do that, do the players who attacked me, looking for PvP, have fun? Is it fun for them to try and fight a player who refuses to fight back?
Having a mode where I can be sure I'll avoid PvP altogether sounds great. Having reduced rewards feels like needless punishment. (Saw someone in this thread saying people who want PvP free modes want all the reward with none of the work - but this is a game, why should it feel like work?) There are already things that mode will restrict people on - lots of commendations would be impossible to achieve in such a mode, and as an achievement hunter I would still engage in the core mode to get those. Making two distinct modes would make everyone change the way they engage with the game.
Currently for me, PvP is a hassle I have to avoid in order to play the way I enjoy; and it's like that because I have no other option. If I HAVE the option to play a safe mode but CHOOSE to play the core mode, my outlook is completely different! I know this because the hourglass feature has demonstrated this for me, it helped me rediscover my love of ship combat (even if I still dislike boarding and sword/gun combat) because I was actively pursuing it!
The people who argue that PvP is core to the game are ignoring the fact that it absolutely doesn't have to be. Perhaps it has to be FOR THEM. But plenty of players (as shown by how dang often this topic comes up!) love the game WITHOUT it. Having two modes would just mean they wouldn't need to interact, which is a net positive for both parties - PvP haters can avoid it and PvP enjoyers can enjoy it with each other. The core mode won't die because there will always be players who want PvP. If you keep Reapers exclusive to that mode too you'll definitely keep plenty of players coming to that mode too.
I don't really understand the vitriol thrown at people who want a PvP-free mode. It wasn't the original intent of the game, sure, but that would stay alive in the core mode. Some people say it goes against the pirate fantasy - again, the core mode would still be there for that, but also, literally everything else about this game is pirate fantasy, and attacking other pirates is just one part of it. I mean historically pirates mostly attacked merchant ships anyway, not each other (not saying it didn't happen but it was hardly part of the core pirate experience) and there aren't any actual trade routes except for people repping the Merchant Alliance.
People need to accept there are not just multiple reasons to play this game, but there are multiple WAYS to play the game - they happen already, having a separate mode for it just facilitates it, and players shouldn't be punished for it with reduced rewards.