It flickers because the persistence of most CRT screens is less than 1/15th of a second, and so by the time you see the second field, the first field is already diminishing in brightness. IIRC Commodore released (or wanted to release?) a monitor that had a longer persistence.
That's how TV's worked back in the day, yes. It would have led to flicker when you had lots of sharp changes in image content across scanlines, but not otherwise. E.g. filling the whole screen with a solid color, or even a smooth color gradient, would've worked quite fine in interlace modes.
Unfortunately, this inherent limitation of interlaced display went unrecognized in the Amiga dev community - everyone would've known that interlaced screens tended to flicker a lot but most devs didn't know why, or how to properly work around the issue.
(Similar to running unscaled High-DPI today on systems that weren't designed for it out of the box.)