Everything we've put into that level of orbit is falling, it is just falling so slowly [...] go from a spiral to a more dramatic arc [...] Once within the atmosphere
This is not correct.
Anything in orbit, is constantly free-falling at barely less than 9.8m/s².
"Orbiting", is having enough lateral momentum to keep missing the Earth.
In the absence of an atmosphere, or any other external influence, an object would keep orbiting forever.
However... Earth's atmosphere doesn't just end, it gets thinner and thinner instead... up to the Moon and beyond (thanks to the solar wind blowing it out)
The reason for an object in LEO to "fall", as in "decrease its orbital height", is precisely because it's been in Earth's atmosphere all the time!
The reason for a "more dramatic arc", is that as an objects looses orbital height, it keeps hitting ever denser atmosphere, until it ends up losing enough momentum to not be able to complete an orbit, which precipitates things (pun intended).