If a train isn’t sold out, which Amtrak should know, then one should be able to switch tickets to travel on it. It’s not rocket science.
That’s not standby, which is what your original post said. That’s a booking change. And it’s really not that different from how airlines handle it. Same-day change to a confirmed seat, depending on the circumstance, can still require paying the fare difference when flying (at least, that’s how United handles it; I’m not familiar with other carriers).
On airlines, standby is free, confirmed requires a fare difference, if applicable (if no difference, then, it could be free depending on one’s status).
On Amtrak, I have changed my booking to an earlier train while en route to the station using the app. As the fare was the same on both trains, it was effectively a free change. So…I’m not sure exactly what you’re suggesting that doesn’t already exist, other than being able to buy a cheaper ticket and ride a more expensive train with it.