It is indeed a catchup mechanism.

The way FF works, gear becomes irrelevant every 6 months, give or take (every pair patch). So having the gear is not really your final goal for doing Shinryu, V3S or V4S. Because that goal becomes irrelevant in a very short span.

If you really aren't completely motivated (with just the achievement) to go in there, that's ok. What could be a relevant goal related to gear, to help keep the motivation, would be to have it before a certain amount of time, like you know a race when the new raids come out (why do you think people are so hyped by mere patches ?Because it's the thrill of purpose coming back). The sooner in BiS, the better the parses and the way fflogs work you'd want to kill the floors asap to take a spot in good logs, and gear is significant (with the same "skill" a guy in 320 will do 15 to 20% less than a guy in BiS).

Since BiS can only be reached with raiding, I'm ok with this catch-up mechanism allowing you to have the same ilvl, but later and not in BiS. With Relic armor coming up though, might change my mind and advocate for a 5 ilvl difference (because if relic armor is also customisable like relic weapon, BiS would become irrelevant with 2 major pieces adjustable and raiders would not have the adequate rewards for the effort)