Should there be a law that if one car stops at a pedestrian crossing all must do so even when the pedestrian is not yet in view?

No. Why would you stop if no one is there? When someone is visible they need to make sure they let them safely cross. But it is the pedestrian, that needs to make sure they can cross safely, before doing so.

No, pedestrians should wait for an opening in traffic, then cross. I've heard of too many tragedies or near tragedies caused by pedestrians who feel they are immune to 2,000 pounds of steel moving at 25-35 miles per hour. Pedestrians have the right of way in a crosswalk, but that shouldn't extend to them stopping traffic just to cross a road.

Which means that you are substituting the judgement of the other driver for your own. No, I think responsibility for their own action remains with a drive. And they are responsible for judging what may, or may not, appear from areas they cannot see. If they could not safely avoid a hypothetical pedestrian a hidden area, tehy must stop - on their own judgement.

In Britain you are not allowed to overtake in the area leading to a pedestrian crossing (I think it's 25 metres) so, in effect, the law you propose already exists there.

Not really.

It would just further hinder the flow of traffic.

There are already too many traffic signals.

Each time a vehicle comes to a stop and starts again, it consumes much more gasoline.

To make it mandantory to stop at each pedestrian crosswalk, is needless, at this time.

Its working just fine on an individual basis, as needed.