The original idea for stardates was that they'd be tenths of a day. I always assumed that they were measuring the ship's time out of space-dock, that they weren't a calendar. I do wish that idea had survived, it was cool, simple and intuitive.
Subjective time out of spacedock is cool and handles any issues with relative time. That's a great and very plausible idea suitable for highbrow science fiction.
However, from a production standpoint, it suffers from one of the main problems that using the calendar date on Earth would. The problem is that there would still be continuity issues involving questions of how long it takes the ship to get from point A to point B. If you say that it takes X days in one episode at warp W, then it has to be that way always, or you have to suggest reasons why not, such as headwinds and tailwinds in space. If the ship goes from star A to star B one week, star B to star C the next week, and then back to star A the week after that, then the triangle inequality
must be obeyed, for starters, or reasons suggested for why it isn't. It just gets very complicated.
In short, the ship can no longer as believably travel at the speed of plot, which it really needs to, because things get nailed down too specifically.
The genius of stardates was that they didn't
make sense. That was by design, to allow the illusion of continuity to be maintained without needing to be meticulous about it.