A hosted AI service is, in most configurations, a processor you have sent your data to. That is workable — the paperwork exists and is routine — but it puts a permanent set of obligations in place: a transfer assessment, a sub-processor list, a retention position, a deletion path, and an annual review of all of them. Each is a conversation, and each recurs.
On-premise removes the premise rather than the paperwork. If the model runs on a server in your building and the network has no route from it to the internet, then there is no transfer, no third-party processor in the AI path, no sub-processor list to maintain, and no retention question about somebody else's logs — for the AI component; the rest of your processing record is unchanged. The security review changes from can we trust this vendor with our data to is this server configured correctly, which is a question your team already knows how to answer.
The second change is economic and it compounds. A hosted API charges per token forever. Hardware is bought once and then costs electricity. That means a workload that is uneconomic to automate at API prices — reviewing every document rather than a sample, embedding an entire archive, running an agent over the whole backlog — frequently becomes economic the moment marginal cost approaches zero. In our experience the most valuable consequence of going on-premise is not the saving on existing usage. It is the work you start doing because it no longer costs anything per unit.