A working AF reduces VMCa . This is reflected in AFM, where also TO distance will change accordingly between a dispatch with AF working and AF not working, due to different VMCa
The TO speeds and distances based on a working AF are lower than for the same a/c with the AF not working –can be even 20 KIAS.
Knowing that AF work, allows the scheduling of lower TO speeds , and use of shorter runways.
In order to ‘know’ the functionality f the systems , the manufacturer/CAA/FAA can require a check every flight , or every day , or every xxx something, and if you need to use the lower speed schedule, you need to do the AF test as requested by the manufacturer