Hi Benjamin,
Seán here from Shopify.
I understand how frustrating it can be to organise orders, particularly once they get to beyond the 1500 mark. To shed some light on why orders can't be deleted, the reason is that no matter when or where there will always be a record of the order in your Admin. This is a security reason, so that you can reference the order at any stage if the need arises.
To help with organising the Orders section for your store, I've had a look here at some options and found the Edit Order app, which allows you to make edits to existing orders from within the Admin. This app may help to make changes in regards to adjusting the orders in accordance to the article examples listed.
It has a 14-days free trial, so is definitely worth checking out to see if it can help. It's also fully supported by the app developer who can be reached by the 'Get Support' button from the app's page in the store.
Another option available is to filter your orders list by using the 'Filter orders' option to select a specific order status, and then save this search a tab along the top of the Orders page.
Hope this helps - feel free to get in touch with the Guru team if you have any questions.
All the best,
Seán
Shopify Support Guru