Unlike other MMORPGs like TESO, Neverwinter, etc. Purchasing a character is actually purchasing the right to create one, not the right to have a 4th permanent character slot. This is mainly to prevent getting more daily rewards, etc.
Phantasy Star Online 2 isn't the only MMORPG to do this. Final Fantasy XIV is technically the same way, in two different parts of its features. You only get one character per world/server on FFXIV if you do their "Entry" Subscription, and only up to a certain amount of characters. While their standard subscription allows up to 8 characters per world/server with a MUCH higher character limit. If you go from standard to entry, and have more characters than allowed, you will be restricted to the last character(s) you logged into last. You will also be unable to create new characters on said worlds/servers.
In addition, their retainer system (basically their "Auxiliary" system), is limited to two free per character, and you can pay a subscription free that merges with your normal access subscription fee to have more. (1-2 USD per retainer.) Once you cancel the retainer subscription, and it runs out, the additional retainers become inaccessible (you can still remove items, but not store anything.) If you delete the additional retainer after this, and attempt to create a new one over and above your two free retainers, the game will not let you.