Most of what you claim here is false. The one truth, that the conversations are not put on open servers, but that doesn't mean classified servers. Calls are not classified and then unclassified, instead, they are evaluated prior to being placed on a server and classified only if classified information is present on the call -- and having classified information on a call of this type is rare.
There is a White House server that is specifically used for calls with foreign heads of state. Naturally, access to the server is limited -- though it still allows many in the White House and State Department to access the call transcripts, those that need to know what was stated as part of their job. To limit access does not require the call to be Classified.
Only if the call actually contained classified information is it put on a classified server. This call was classified to limit the number of people that could see it -- only a very small number of people, essentially top White House personnel, were able to see this transcript.
