Honestly as NYT subscriber I really doubt that people actually read NYT through archive or at least most of the archive reader wouldn’t convert anyway. To me it seems like a bad sign of them trying to hide something. Archive is a public way to track website changes which is very valuable for validating journalism.
In general NYT is trying to have their content public and take advantage of indexing but also private for selling subscriptions. It’s a bit of a paradox that really diminishes their position here.