Was it not common to have some kind of device that enabled the driver to set the points from the cab? -- I seem to remember reading that it was done by either drawing power, or not doing so, at a particular point on the approach to the points. (I do though remember once seeing a tram driver changing points manually somewhere on the Continent, presumably because something had failed to work properly).
Yes there was, presumably drawing power on the straight route as that would have allowed a higher speed. But it can't have been foolproof, for example if someone stepped in front of the tram so they had to shut off power on the critical section, they would then have had to stop and use the point iron. On more modern systems the driver can select the route using a keypad in the cab, that (on all the ones I know about in detail) operates a transponder that sends a message to a wire loop between the rails. There was an incident a few years ago where someone caused havoc in a Continental city by using something like a TV remote to operate the points, so presumably a different system was used there.
However, as I mentioned above, points at either end of a single line would have been sprung as all trams coming off the single line would (in the UK) take the left-hand track, so none of these would apply. In any of these cases the tram driver is still obliged to confirm that the blade is fully home in the correct setting, either by direct observation or via an indicator, as tramways lack the sort of high-integrity signaling and detection provided on railways.