The intent of a collected addressbook is to collect addresses you don't have in default addressbook so that they are available when writing messages. And Thunderbird is doing exactly that. What you're indicating is that you want to collect the addresses, but not use them, and you're wanting Thunderbird to work differently so you can continue collecting addresses you don't want to use. My suggestion, considering how Thunderbird actually works, is to stop using the collected addressbook and selectively save new email addresses elsewhere, or to periodically review the collected addressbook and purge unwanted ones.

I have several address books, but all addresses from all address books show up as suggestions when I start writing a name.

But I want only specific books to be used/not used, depending on the account I am writing an e-mail with.