For common monster, I prefer the actual system. what I write below it's about notorious monsters.

I have experienced different ways of claims.

1. First hit takes exp/loot. Everyone can help but takes nothing.
This system has a "problem", if you have an high level char as friend, you can exp really fast: you hit, he kills.

2 First hit takes exp/loot. Everyone can help, but takes nothing, but decrease the base exp taken from the first one.
This is the system used in a lot of games (this one, not the first one). The problem is the opposite of the 1., there will be someone "stealing your exp". It's not important if the exp comes from quest rewards, but it can be a problem if the exp, as in FF14, comes from monsters.

3 First hit takes exp/loot. No one can help.
The actual system in FF14.

4. Everyone takes exp, everyone take loot according to the damage dealt/suffered.
this is the system I prefer. Example with numbers:

- Boss monster with 8,000 HP, during the fight he hit for 2,000 hp (direct damage). 10,000 xp total.

Group 1: G1 tanks the monster and the players hit him for 3,000 HP
Group 2: G2 doesn't tank the monster and the players hit him for 4,000 HP
Group 3: G3 deals only 1,000 HP and the monster die.

so, the group 1 takes 5,000 xp
the group 2 takes 4,000 xp
the group 3 takes 1,000 xp
In the same way the loot will be shared. If there is a RARE item, it will be rolled
50% for G1
40% for G2
10% G3
However It's possible to give more weight at the tank damage.
What does happen with this system ?
If we find the monster before the others, we can start to dps and tank, and if we are enough fast, the others will take only crumbs. However, not knowing at what point is the monster, every group will help killing him (and not only cursing the first group).

5. Everyone takes exp, the player who does the bigger amount of damage takes the loot.
similar to 4, but if we want loot, we have to damage at least a % (20% or more). In the example, only g1 and g2 take loot, g3 takes only some exp.

About Behest.
I think the actual system works. We can do a party, and kill the monsters together or be greedy and try to kill everything with our little party. The best idea I have seen is the so called "public quest" party, where, when an event starts, an invite for a new party is prompted to everyone.