To put this into historical context, it's worth pointing out that the ability to set the seconds is more a matter of convenience than one of precision timekeeping. Historically, the most precise mechanical timepieces (e.g. chronometers, astronomical regulators) routinely lacked seconds-setting mechanisms, or even a mechanism for precisely regulating the rate.
Precise timekeeping was achieved by periodically comparing the timepiece to a time standard (e.g., the stars), recording the how much it was off, and using math to apply these values as corrections to the times you read off the clock. Once you're going to these lengths to obtain precise time, the ability to set the seconds hand doesn't really do much for you.
In fact in this context it may even make things worse. Many such mechanisms interfere with the stability of the balance, which means that they detract from timekeeping precision. And if you reset the time you then need to record when you did so, the error before and after the reset, and apply these values as a further correction to your data. I.e., you end up doing more work for little or no benefit!
Settable seconds, as I understand it, first became a common feature in aviation and military timepieces, because in those situations you don't generally want to be doing a lot of math. Settable seconds allows you to synchronize your watch to a master clock (or to your colleague's watches, as in the movies) and then be confident that it won't drift too far off during the next day or so.
There's probably some interesting history here also about public reference clocks—accurate clocks that were put in public places for people to set the time by—but I'm not the one to tell it. I do know tidbits like this one: Big Ben is kept accurate by measuring how far off it is from the correct time and adding/removing weights from its pendulum to alter its rate and thus steer it toward the correct time.
And for ordinary laypersons' timekeeping needs, seconds don't really matter, so old watches just don't have anything for this.