If I recall correct, from EV12.2 you have an EV Powershell command called Export-EVArchive. There also is a 'get-archive', so you might be able to do some piping..
Exporting 1000's of archives will put a huge load on your storage servers. You need to make sure the archives to be exported are not too large, or have zillions of items. If you indeed need to export 1000's of archives, then you might want to look at a 3rd party application to do this. In addition, if you want to export to move them to 'somewhere else', you might want to look at migration software (Cloudficient/Transvault).
That will save you head-aches.
If you still want to use builtin functionality, keep in mind it is not fast. 1000's of archives might take months to finish.
I concur with Gertjan, if you are dealing with 1000's of archives then a third party app such as Transvault or Archive Shuttle will make your life much easier. The thought of exporting that many archives with EV's built-in functionality sends a shiver down my spine, even with scripts it would be labour intensive.