I understand that. Adapting Rust to better suit domains it hasn't considered much is a language design problem, which is off-topic for this forum; airing concerns and figuring out how the language can change to address them is the purpose of IRLO, which is why I directed you there.
The closely-related issue of working around Rust's current limitations in unusual (for Rust) situations is on topic here, however, so that's the flavor of response you'll get. For the purposes of URLO discussions, changing Rust isn't a viable option— Lobbying and waiting for a language change is too slow of a process when you're trying to solve an actual, current, real-world problem.
It would also help if you clearly state that you're working in a specialized domain. Most of the responses have directly answered the root question you asked in the title, "Why is
std::time::Instant opaque," with the reasons the current design was chosen. These answers have necessarily been couched in general terms because you've given no indication of the domain you're working in.
Even now, after reading a fairly long thread, I have no idea what "your field" is, so there's no possible way for me to anticipate which of many potential concerns will be important to you. By definition, you're the expert here in your field, so it's your job to educate us about any specialized requirements you have. Barring that, the advice you receive will necessarily feel like a bad fit for your situation.