Change default to exclude archived contacts in advanced search
Change ADVANCED SEARCH to search only current contacts by default. I suspect most searches are run against current contacts and therefore must always use the "NOT ARCHIVED" criteria. This would also solve the problem that there is no way to exclude archived contacts when searching using "ANY of the following criteria".

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William Nemmer commented
This could also fix the problem of emails being sent to archived contacts. Currently you need to include the "NOT ARCHIVED" criteria in an advanced search of contacts.