You know, we could have a happy medium here.

1) Any free company can attempt a "special" primal battle in order to get that primal's card. There are unlimited amounts of cards available, so every free company on the server could get the card if they defeat the primal in the special battle.

2) Once a free company gets the card, that free company can enter into a blood pact with that primal (so the primal can get the card back).

3) Once the blood pact is entered, summoners from that free company are able to summon that primal's avatar for one earth week before the pact expires and another card must be obtained.

If the special primal battle was sufficiently challenging, it would still be a rare sight to see ifrit's or leviathan's avatar being summonable by a player. Furthermore, once entered into a pact with one primal, it would not be possible to enter into a pact with another until the first pact expires. (or entering into another pact cancels the first)

This way, summoners can be happy, avatar's can be rare, and everyone wins.