The PC has always been one of the most important elements of Pokémon, but its original incarnation was anything but user-friendly. Because the PC is essential for the player's Pokémon-catching journey, one would assume that the developers would make it easy to use. However, the original version of the PC had some issues that made it more frustrating than necessary to deal with.
In Pokémon games, the player can only carry six Pokémon with them at a time. If the player catches more, they will go to the PC instead. The PC serves as storage for all the player's Pokémon outside their active party. While in the PC, everything about a Pokémon, from their level to their moveset, remains the same until the player brings them back into their roster of six active Pokémon and starts leveling them further. It's thanks to this system that players have a chance to catch 'em all like the series' tagline implies.
In the first two generations, the boxes in the PC that held the player's Pokémon had a limit of 20 Pokémon per box. At first glance, this would not be a problem, but when a box filled up, the player would have to manually switch boxes. This meant going to a PC and logging into the system to switch boxes. The game also saved every time the player switched boxes, which does not sound like a hassle, but the early Pokémon games needed an extra few seconds to save. When one had to take a break from catching one of Red and Blue's Legendary Pokémon to backtrack to a PC, that extra time could be annoying to wait through.
Pokémon's PCs Used To Be An Obstacle
This issue with being forced to switch PC boxes had one annoying side effect. When the player's current PC box was full, they would be completely barred from catching any more Pokémon until they switched to one that had room. While this could be handled by going to a PC, it's possible that a player could forget, and that would lead to dire consequences. It's entirely possible that the player could come across a rare Pokémon like Phanpy, but be unable to catch it due to their current box being full. This would be even more heartbreaking in the case of a shiny Pokémon, considering how scarce and sought-after they are. Legends: Arceus may have made catching shinies easier, but they are still incredibly difficult to find in most games.
Thankfully, once Generation 3 came around, the old PC box system was replaced with a far more efficient one. Starting with Ruby and Sapphire, whenever the player would catch a Pokémon, they would go to the first available spot in the PC. The fact that the player no longer had to manually choose a box also meant that the player would never be prevented from catching a Pokémon unless they had managed to fill up every single box. Considering that a player can play through an entire game and not come close to filling up the PC, it seems unlikely that would be a concern for most, even if Pokémon gets better endgame content.
The Generation 3 update to the PCs in Pokémon games took them from being a necessary chore to a pure convenience. Removing the need to manually manage PC boxes greatly streamlined the process of catching Pokémon. Thanks to the improvements of Ruby and Sapphire, the PCs of Pokémon are no longer the most annoying part of the catching process.