Are you sure this isn't just the convenience start feature? The V12 & V8 BMWs starting with the e38...has a feature that only requires turning the ignition to the start position (KL 50) then you can release the key and the starter will continue until the engine starts.
If you are having issues with the engine not starting...it can be disconcerting to hear the starter continuing on when you've let go...but this isn't a starter issue...its a feature...and the issue is more about why the engine isn't engaging...not about the starter.
You can see this feature mentoned in the owners manual (see text highlighted in green below) and in the EWS info below. In the EWS chart, its called 1-touch start & started around the 1997 model year...then gradually was added to other models with V8 engines as they rolled out. The I6 and manual tranny V8s didn't get this feature: