Single page order submission ("checkout") for a site that doesn't use addresses or payments

[thisisjamessmith]

I've been trying to make a single page "checkout" process in Commerce for a site that won't take payments, and also doesn't need to collect addresses. What it does need is the option for users to register an account during checkout. I assumed this would be very straight-forward in Commerce but I've come across a lot of problems.

Specifically, I want all users (regardless of whether or not they tick the box to register an account), to have their User element populated with their name. The only way I've found to do this successfully for users who tick the box is to have a two-stage process where they first add their email address and then full name into a field named billingAddress[fullName], along with some dummy hidden billing address fields to appease Craft's required fields for billing addresses (even though I don't really need a billing address), in a form that uses the commerce/cart/update-cart action. Then in the second step they can choose to tick the registerUserOnOrderComplete box and complete their order using the commerce/cart/complete action.

Problems:

1. For users who don't tick the registerUserOnOrderComplete box, the Full Name field in their User element is never populated.
2. I shouldn't need to create a dummy billing address for this.
3. I should be able to do this natively in a single form submission, not two.

Have I missed some simple/obvious solution to this? It seems like a lot of work for a relatively simple thing.
Some related discussion here: https://discord.com/channels/456442477667418113/456442867163070466/1062341996729081896

There is also a semi-related issue here, which prevents me from using firstName and lastName as separate fields in this setup, as is possible when dealing with Address elements: #3015