Interesting question! The cases I can think of are , , ,
> It's faster to walk than to take the bus
>
> You need a visa to go to Japan
>
> Even if it's true, I'm still concerned
>
> This is necessary for participating
There are probably others.
As to why zero-nominalization occurs, I'm not sure. But it seems like it's an old construct in Japanese, which used to be more prevalent, but now only survives in certain combinations. So an more interesting question might be why it started to disappear.
would mean "do it well/do it often/make it well". would mean "make it a good one/choose a good one". I'm not sure if it's to distinguish from these cases that zero-nominalization survived here, but it might be a theory.