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Assigning bills/expenses to a customer has too many unnecessary steps.
1. Open bill/expense
2. click on assign to customer
3. select customer, you cant use the drop down until you type (part of) a name
4. select an expense even though it already shows in the window (remember, we were already in the expense in step 1)
5. Click on assign to customer
6. click on ok.

If you select the customer and click ok, it will not be assigned as you missed step 4 and 5. It is not intuitive at all. 1, 2 3 and 6 should be more logical.

Invoices have a field for the project, why not bills, expenses and manual journals? It seems farily fundamental to be able to allocate any transaction to a project.

Completely agree with this, there seems to be an extra step that is unnecessary and I miss it most times and have to go back and do again

Hard agree!!!!! it takes far too many clicks everywhere to assign anything to a project.

It shouldn't be so difficult to assign expenses to customers or projects, an expense or spend money item shouldn't need to be edited to add it to a customer or project.
Simplifying this process could be as simple as an extra column that can be enabled on the Account Transactions view and if a transaction isn't assigned to a project or expense then it can be simply clicked in the column and the customer or project selected.
Additionally Bank Rules should be able to include the option to assigned to customers or projects, if we have a client that charges parking at a specific merchant which we can pass the cost back to then the rule should allow this kind of assignment.
We use Airwallex for our employee expense management and we require most of these transactions be assigned to a project, this means we have over 200 transactions a month we have to manually edit to add the project or customer, it's a significant time burden and completely unnecessary.