It's not nearly that easy. Multi-lane highways generally aren't next to the existing train stations, so in addition to the infrastructure of the track, you'd need to build all the stations, plus the roads and parking to reach those stations. Even if you just want to make the station an exit off the highway, that's still a lot of expensive infrastructure and additional space, beyond just trading a lane of highway into a rail.
I've long thought that the interstate media would be the perfect place for passenger train rails. Then visited Chicago and lo and behold they did that with their commuter trains.
My imagined version has the trains running in the media with under passes to stations located in towns along the route.
We'd love to have a train to ride from here to the big metro where we attend concerts and other entertainment. Attend the concert and ride home to our town sleepy or tipsy with no problems. Right now I drive DW/teen/friends to the concerts and then park somewhere nearby. Grab a coffee and/or sandwich (use their wifi) and nap. Saves a little on parking, and I'm 100% good to drive while they gleefully recount how great the concert was and fall asleep.
I assume you mean median, but if you meant something else let me know and I'll adjust my response.
Not all interstates have medians, particularly when going through cities. 95 runs from NY to FL, and runs directly through the centers of Philly, Baltimore, Wilmington, etc. Going through those cities, the highway is frequently elevated above the city, with the regular city streets passing below it. If you're really lucky, the Amtrack line runs parallel or beneath the highway, but mostly it doesn't. (I can't tell if the street view photo I tried to attached worked or not, but this is the view from a city street. That overpass IS the interstate. Where would you like the train to run?)
I'm sure it could work in younger cities, where the city was built around the highway, or in better designed cities where the highway passes beside the city with a beltway or other access road, but the east coast isn't either of those things.
It's not nearly that easy. Multi-lane highways generally aren't next to the existing train stations, so in addition to the infrastructure of the track, you'd need to build all the stations, plus the roads and parking to reach those stations.
MEEEEPP! US confusion! You don't need parking spaces at a train station! Well, a hand full for Taxis and a bus loop. But that is way less than your average clover leaf.
Not to mention: If the US is known for one thing, than for the amount of space. Just look what all the single family houses are using! The vast stroads! Space galore!
I mean, if it is for a new highway (lane), the "space" problem is the same, just worse, and those are still build, so it's not like it's physically or legally impossible.
Worst case, build the trains above the highways. Or under. Works in other places, so why not in the US? (btw. In Tokyo train lines are build above rivers (well, canals)).
Yeah, that's not going to work in the US, where bus travel is universally reviled, whether it's actually terrible or not. Convincing people to haul their suitcases on a bus, in order to transfer to a train, is definitely not going to happen. Not having any parking at the station is a great way to guarantee no one uses your train.
The US may have a lot of space, but someone owns that space. There's a huge amount of pushback against the government using eminent domain to seize land for projects like this, and even when they do, it's hideously expensive, because they're required to compensate the owner for the appropriate value. And it actually is very difficult to add new lanes to existing highways, if the government doesn't already own the land on either side. The difference is, you can add the new lane for just a few miles where the land is available. A train line that runs only a few miles won't be much use to anyone.
I'm not saying it's physically impossible, just that it's politically and culturally impossible.
Like I said before, I would personally love it if trains gained traction - we regularly walk to the local train station, and the last few times we've flown we've taken the train to the airport (and that's been a few years now). In fact, I'm going to be walking to the train this afternoon to get into the city. But public transit here regularly takes twice as long as driving, is less comfortable, and requires a lot of waiting around in dirty, uncomfortable spaces. I'm six months pregnant and will likely be stuck sitting - or even standing - in an un-conditioned space for over an hour in 85F heat, waiting for connections. You can't really be surprised when people decide not to go with that option.