This is a good question! The main reason why we charge on the 1st is that is allows us to aggregate patrons pledges. This significantly reduces the fees that creators pay since many patrons support multiple creators.
The honest answer to your other questions is that payment schedules are a giant can of worms and it’s very hard to disentangle. But if you want to dive into it, I’m happy to try and share my limited knowledge about it with you!
To be able to charge patrons using anniversary billing (that is, every 30 or so days on the day they joined, not tied to the calendar month) we have to de-aggregate payments. This is what Patreon had planned to do back in December 2017 but we ended up rolling back due to community upset. In the announcement post of that change, Patreon said: we need to move our payments system to treat your pledges like any other subscription service. In other words, we need a system that charges patrons at the time of their initial pledge, and on the anniversary of their pledge each month thereafter. However, the feedback to this change proved that it was not popular as it would have disproportionately impacted $1 – $2 patrons and that aggregation is highly-valued, which we underestimated. This blog post (it’s not from Patreon so I can’t vouch for the accuracy here) goes into more detail about that change.
We know that anniversary billing is highly requested and it’s something we continue to think about and explore on how best to solve. As shared in this other thread, we’re starting to explore more payment options on Patreon (both currencies and format) - currently in beta is the ability for patron to pledge annually, not monthly.
@Sierra_Vandervort to turn on charge-up front, this help article has info! But remember, it’s a permanent change like @how2rhino says. We try to make that very clear in both the help articles and the product when you make that change.