Originally Posted by Fajita Dave
Bikes that have to be held down with constant pressure on the bar is due to the geometry (mostly bikes that have a lot of trail built in for stability). How the suspension compresses in a turn and tire profile have a heavy effect on this too. When the front tire on my sportbike gets worn I have to hold it down into the turn. Its perfectly neutral with a new tire to the point I don't even need my hands on the handlebars.
I have 4 road bikes, an 08 KLR, 87 BMW R65, 02 BMW R1150R, and a 96 FLHTP. Each of these bikes will tend to right themselves and go straight as soon as I relax or release pressure on the bars.
I can't imagine riding a bike that was "neutral", if by "neutral" you mean it requires no effort to put it into a turn or hold it there.
I don't know enough about bike geometry to discuss specifics, but I do know that the gyroscopic effect of the front end geometry wants a moving bike to stay upright and run straight unless directed to do otherwise by the rider.
How much effort it takes to turn in or hold a turn can be debated, but if it requires no effort it would be a dangerous bike to ride, in my opinion.
I believe that many bike accidents that occur in curves are caused by a brief moment of panic when the rider thinks he can't make the turn, relaxes momentarily, and goes straight into a ditch, guardrail, oncoming auto, or whatever. Experienced riders will apply a bit more downward pressure on the down end of the bars and complete the turn.