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This is so important, a billable expense is so easily missed. Deleting an entire draft to add a few items is inefficient to the extreme.

If we are billing expenses, we should be able to attach the expense copy added when we create the expense to the invoice.. just like we can add attachments to regular invoices.
Very inconvenient that this isn't possible.

Is it not possible to create an invoice, and add project time or expenses to it?
A drop down box under the heading of something like "Add Project Time/Exp".
Drop down box would allow you to choose the relevant project and would take you to the unbilled time / expenses screen.
From here you could select the time or expense you wanted to add to the draft invoice.

Goodness, I can't believe it is not possible to edit (add new time entries) to an invoice created in Project

Additionally this would allow for recurring invoices to be setup to save as draft and then be able to add expenses from projects to those draft invoices. I use recurring invoices to ensure I don't miss an invoice but occasionally the line items will change which is why it is critical to be able to access expenses assigned to a project from an invoice not created via the project.

It would also allow a single invoice for multiple projects which is currently not possible either.

The fact that costs that are set up within Products and Services come into Projects as a "% Mark-up" item, even when they've been set as "Non-Chargeable", means that errors can easily be made in then changing the "what you'll charge" dropdown, marking things as non-chargeable when they are chargeable. If we find errors in this (and there are several monthly) we therefore have to delete the original draft invoice and replace it with one that has all the chargeable tasks and expenses on it, rather than just adding the additional item(s) to the invoice already created.

Agreed. Those that are entering expenses (say through Xero Me app) are primarily focused on capturing the expense, and if using own money, getting reimbursed for it.
Assigning to the right customer or project or one at all depending on the setup is not often a concern or confusing. fact fields are optional makes it more so.

At invoice time those responsible for invoicing should be able to pull expenses from where ever they sit and add them as needed