If you search for a character that has 1 rank 50 class at the moment on ffxivpro you'll notice that their rank on the server is probably higher than 2,000. That of course means that there are more than 2,000 people with a greater amount of skill points acquired. Some of that is crafting, but a large portion isn't. Then consider that 2,000 doesn't track everyone. As an example, if 1,000 of those have 1 rank 50 combat class (highly likely and conservative estimate), and they all want to get in to the dungeon some day during a single 24 hour period then that's more than 40 players trying to get in per hour (spread evenly across the day). That number drops in off hours and increases at prime time for EST and JP time. at least twice as many people play during prime time, so I think it's highly reasonable to say that 80 people could be trying to get into an endgame dungeon per hour during prime time.

Now consider that my estimate only involves people trying once and then either succeeding or giving up. People will continue to try repeatedly. Many of those people could try all day long. There are some unknowns there, but it would be very easy to push that figure up to 200-300 players trying to use the dungeon per hour during prime time. If there aren't enough instances to accommodate that then there are going to be a lot of unhappy players.

Finally - keep in mind that it's SE's goal to INCREASE the number of players, making this issue even more important for their future. Players will probably come back to FFXIV to try this content. If they find it inaccessible they'll say 'lol' and forget about FFXIV forever.