The plane turns while banking which results in a force vector mostly straight down towards the floor. If the plane did not turn while banking what you wrote is true.
A coordinated turn with 60 degrees bank should be achievable by any airworthy airplane (it requires pulling 2g), and the maximum bank angle for a steady-state coordinated turn depends on how many g you can pull before you run out of control authority, cause an accelerated stall, or reach the airframe's structural limit.
Next time you fly, get a beverage of your choice and observe how it behaves. Here's an example, courtesy of the great test pilot Bob Hoover:
If the turn is coordinated you can't tell the difference. I've been in small GA planes turning at 35-40 degrees and it doesn't feel like you're sliding at all, you're pulled back into your seat and "down" (relative to you) into the flooring.
