This is an incredibly naive mindset. How can everyone "try harder" when no one has the slightest clue why they reached enrage? You mention having only really done Extremes. So here's the thing. Extremes have a comically low threshold to clear. Rubicante can allow upwards of like 8+ deaths and you'll still make the check provided everyone knows what they're doing. This is very much not the case for Savage, especially in the early weeks. Even after the nerf and three weeks worth of gear, you'll still see enrage without everyone pumping in P8S. You really can't compare the two until after you start getting gear which neuters the DPS check quite significantly.
A party leader is under no obligation to give you any chance. In fact, they can kick you simply for disliking your glamour. It's their party after all. Now most parties won't kick immediately and give people a chance to work out whatever kinks they need but if you're messing up several times then it's well within their right to rep you. Although, even in such a scenario a lot of people will simply disband and possibly reform with the good players.
Let me give you a scenario I ran into a while back that really highlights why parsers are so useful.
Back near the end Shadowbringers I was helping a friend clear TEA. Now three of us were using relics and nearly everyone had dungeon BiS which is a massive upswing in damage from when the fight released. Nevertheless, we still saw enrage clean on more than one occasion. Which just shouldn't happen. I cleared TEA on content with far less gear. So the raid lead and I started looking through logs to determine the issue. Turns out neither healer had optimizing their healing and were essentially healing over each other and not dealing damage. They were a combined 2,000 below expected DPS relative to other groups. My co-tank was also struggling. Without ACT and FFlogs, you'd be inclined to put that blame on the DPS since it's a DPS check and all. They were all fine. Sure, they could have pumped out a little more but at that point you're squeezing blood from a stone.
Once we sorted out that issue and the healers focused more on improving their DPS, we cleared.
At the high-end level parsers are simply far too valuable a tool in a game centered around DPS. I can assure you their removal would actually lead to more toxicity because now you'd have people blindly pointing the finger at each other without any idea who's actually struggling.