ABS does not stop you falling off.
It also cuts out at slow speeds where its effectiveness is nil.
The main value of ABS is where you need to stop from higher speeds and a skid at the front wheel will slide the front out from under the bike. When the ABS senses a lock up it reduces the brake leting the wheel grip and prevents it sliding out.
These things happen so fast the ride might not even be aware of the system working. A friend with a new Honda 500 arrived at work after a wet ride complaining his brakes were stuffed, they kept vibrating. Little did he realise his ABS probably kept him upright and got him safely to work.
2001 Yamaha Zuma, DR Evo 68 cylinder, Leo Vince TT derestricted, Delorto 17.5 (#98 jet), standard aircleaner, RMS fan, Race CDI, Standard oiler and premix @ 75:1 Shell SX2, Doppler SR3 variator, RMS clutch, RMS R rear shock absorber and Pirelli SL26 tyres.