The 2.0 primals had a lot of longevity and were fun because the weekly primal quest, ponies, and other goodies you could get by running them.

Let's also include up to 3.0 and look at the rewards for each of the primals in related to the other things you could get in the same tier.

2.0:

Ifrit HM dropped ilv60 weapons.
Garuda HM dropped ilv70 weapons.
Titan HM dropped ilv70 weapons (was later increased to ilv80).

Relic weapons were ilv80 at base, and ilv90 upgraded. 
Allagan weapons were ilv90 (later increased to ilv95).

Yes, the relic required you to go through the 3 primals and it was recommended to have at least the Ifrit or Garuda weapon to get. You might also have had the Titan weapon. Regardless, the weapons weren't used for very long even after you did get them. They were better suited for your alts whilst you worked on their relics.

2.1

Moggle Mog was added, which dropped ilv75 weapons.

Not worth really farming for outside of glamour. You most likely had your relic, or if not you were working on it.

Garuda/Titan/Ifrit Ex was added, which would reward you with an i90 for beating all 3.

It was definitely easier to get an upgrade relic by this point. Titan EX still to this day is hard for some players. Those who could clear all 3 easily enough each week could get themselves an i90 for their alt jobs, but most players still worked on getting their relics upgraded.

2.2

New HM primals no longer dropped weapons.

Moogle Mog Ex was added, which dropped an ilv100 accessory (which is moot here). Leviathan Ex was added, which dropped an ilv95 item that could be upgraded (if lucky) to i100.

The new capped tome, Soldiery, offered an ilv100 weapon rendering the 2.0 and 2.1 weapons obsolete. These could be upgraded (though only via a drop in SCoB to start with) People still worked on their relics to ilv90, and would try to collect atma and complete the animus trials to get an i100.

Raiders could work towards an i115 weapon from SCoB or get the upgrade item for Soldiery to i110.

The relic upgrade process was pretty time consuming and brutal, though. Only crazies did more than one during this time. This patch, however, was probably one of the best in offering options for the same tier of weapon and also providing benefits to the hardcore raiders. Casuals has their relic upgrading process. The hardcores had their Coil. And even those in-between (commonly referred to as midcore) had Levi Ex as well, to get a decent weapon.

2.3

Ramuh Ex was added, which dropped an ilv