Why didnt they kill the kid?

Why -- what would that have accomplished? The could have killed the father too, but again, why would they? Both could be used as hostages, as Peter Lorre mentions near the end.

I think a better question would be, why didn't the cops show any regard at all to their fallen comrades on the street? Surely some of them were simply wounded, not killed. Yet there is no ambulance, and the police are shown calmly drinking tea while making plans! It is clear that action sequences were just not that well thought out at this early stage in filmmaking.

I think that by the time the criminals realised their plan had gone haywire, they were too busy fighting off the police to be worried much about the child. And whoever was left after the shoot-out could use Betty as a bargaining tool.

The real question, and this goes for the remake too, is why didn't they just kill the titular Man?

What's the Spanish for drunken bum?

It's an interesting question you raise. There is a limit to the level of darkness the audience will tolerate, even by the standards of the 1930s. Peter Lorre got this role by and large for his performance in Fritz Lang's 1931 M--a German expressionist film about the kidnap and murder of a child in Berlin; Peter Lorre playing in Fritz Lang's 1931 M the role of Hans Beckert--child kidnapper and child murderer. I seem to recall reading somewhere, that Peter Lorre did not like being typecast as some kind of demento as he was shown in Frtiz Lang's M. So it may have been a combination of aesthetic sensibilities being violated and Peter Lorre setting limits on what kind of movie character he would be portrayed as.