That's why the field strength needs to be slowly decreased, or faded out, to prevent leaving any areas with one particular magnetic orientation. That being said, you can always repeat the process (as many times as you want/need) if R/W to scrubbed floppy fails, and frankly it's rather hard to create any problematic hot-spots anyway. The media will simply not accept magnetization over certain threshold, and the heads should be able to deal with it.
The whole idea of scrubbing the media is meant to resolve 2 issues:
1) Remove any readable data that can prevent FDC (or the OS) from formatting the floppy properly. DOS in particular can be pretty stubborn and stupid about it - like refusing to format only 1 side, or the opposite, silently formatting only side 0 if the previous format was such, even on 2-sided DD floppy in standard 360k PC drive, even if using /U. Or just refusing to format at all if it doesn't like something about track 0 residual data.
2) Remove any weird and unreachable magnetic glitches that prevent correct operation or cause bad sectors - for example if the floppy was written to by unaligned drive and now has fresh, strong data in what should be space between the tracks, it can easily prevent some weaker drives from being able to read or write to such floppy. Even normal use in just one drive can create some bit glitches that the FDC can't deal with (most HW has some requirements about sector gaps and fill bytes).
TL;DR: Keep your magnets well away from floppies you do not want erased. On the other hand, if you want a floppy properly scrubbed from any data, a simple magnet will do the job. Might take some practice though.