Attendance events, which are shared among all the characters on the account (per world), give many rewards. Usually a new one every day. It is not required to claim each reward on the day it is earned. However, it is required to claim them in order: you can't get Day 2's reward before claiming Day 1's, even if you've already got stamps up to day 7.

Compare this to events like the Rocket Booster currently running, or the Artifact Hunt and Steamed Bun events we had recently: they also have a new reward every day, they also allow for claiming the rewards later than the day they were earned, and they are also shared throughout the account (per world). The difference is that these events allow for claiming the rewards out of order. You can claim Day 10's reward (assuming you've amassed enough points) before claiming Day 1's.

The rewards for both kinds of event expire, so unless I have an immediate use for them, I generally postpone claiming them until the last day.

The ability to claim the rewards out of order, allows for claiming all the rewards I want on character A, and then switching to character B and claiming all the rewards I want on that. It also allows for claiming the rewards I do have immediate use for right when I earn them, and leaving the rest for later. In short, this method is far more convenient than the attendance method of claiming them in the order of the days.

So, I suggest that attendance rewards behave like point-accumulation event rewards: allow claiming any reward for a day that has a stamp on it, even if the rewards for "earlier" attendance days have not been claimed yet.