Most newsletter tools keep your list on their servers and charge by the size of it. Leave, and you take a spreadsheet of addresses with you. The history, the stats and the archive stay behind.
I built Currawong, a newsletter service for bands, venues and small organisations, the other way round. Your list lives with you. Sending goes through your own account with Amazon SES, Resend, Mailjet or Brevo, so you pay the sending service directly, which for Amazon SES is $0.10 per 1,000 emails. Change sending service and the list, the history and the unsubscribes don't move.

