There's a handful of restrictions to your character actions while a party is engaged in battle. Such as, you can not join a party that is engaged in battle, or you can not change your class.

However, I do not understand is why are you not allowed to leave a party while they are engaged.

Here's a normal daily combat situation I run into. I join an exp party, and play for a few hours. When it is time for me to leave I bid my fellow party members good bye, while they continue the party. I teleport while still in the party so my party members also receive the teleport. After teleporting away, I attempt to leave the party, however restricted to do so because the party is engaged in combat.

Another one which is rather frustrating to deal with is trying to invite someone into a party that is already engaged in combat.

Here's another normal daily combat situation; My exp party has been going on for several hours, one of my members, Alice, has to leave, and has a replacement member, Barret, to fill her spot. As Alice slips out of the party after finishing a battle, Barret tries to join. However, Cid is in a rush to start battling the next monster, and engages the monster right away. Barret is unable to join. Cid is obviously to the fact that Barret cannot join, and continues to engage the next monster.

Additionally it applies to inviting or using the party recruit system while the member is not in the vicinity of the party! Honestly, what can a inviting a party member that is in Gridania do that causes harm to a party that is engaged in combat in Skull Valley do?

I understand that there's a lot of good reasons not to have a party member join a party that is engaged in combat. Such as, that they are able to gain credit for the kill, or obtain loot that they are not credited for, and a slew of other reasons. However, restricting it causes too much of a hindrance.

If you don't want to give them SP or loot for joining late in a combat, then don't give them SP or loot.
If you don't want to give them credit for joining late in a NM fight, then don't give them credit.
If you don't want to give the party a new tier of party boost bonus for a new member joining in mid-combat, then don't.
*Most of those are already enabled if the party member isn't within range or assisted in combat.