Running 2,000 documents a month through AI costs under a dollar in the cloud, about the same on EU hosting, and one €3,000 machine locally. Price does not decide where a document goes; the shelf it belongs on does.
Three quarters of small companies that already use AI use it for one isolated task, and the savings you are looking for sit one step further down the process.
The bottleneck between an impressive AI demo and a system your team actually relies on is not the model. It is architecture, governance, and maintenance.