So, up front you don’t want to track. But you want an API to see where your users have been on your site to target ads. Which is a form of tracking. Yes, internal only, but still tracking.
History is a user preference for the users of browsers to reference. I don’t see a good enough justification for adding site access to it. Even if it is same-origin. I think we’d need more valid use-cases beyond advertising to add a feature. Things that compel a better user experience then what is available today.
As mentioned by @Rockefeller you can use local storage such as indexeddb to achieve what you want today. You’re just coding your own history storage vs asking the browser to give you access to the storage it has. Which, would be the ideal way of going about this. Build a working demo showing how useful your system is, get developers to adopt it, then if it is widely desired browser vendors can assess making this type of feature a core API.