We ship exclusivily with USPS. When a customer checksout, the default shipping application shows "Priority Mail (2 business days)" or maybe "Priority Mail (3 business days)". So at checkout customer assumes the item will arrive by that listed time but it does not show order processing time. It's created confusion with our customers.
Is there a way to either remove the ETA listed (example removing the 3 business day ETA and just showing priority mail) OR is there a shipping application that might address this issue?
To remove the ETA listed you can change your theme language. This link explains how. Use the search field to find all the places in your checkout that use "shipping" language and change it to reflect your processing time.
In addition, if you are looking at adding a fixed number of days based on product type, you can use the Multi Carrier Shipping label app which allows you to create automation rules and add fixed days based on product type.