You're right in the sense that accuracy in the absolute sense usually isn't that important. The problem is drift. Mechanical watches, especially less expensive ones, will gain/lose time at a more or less constant rate. Unless you know the rate and time to the last correction, you're never really sure how far off the watch might be. Resetting your watch every day isn't practical. Also, if it doesn't have a battery it needs to be rewound - either manually or by activity via an internal pendulum.
Electronic watches utilize a high-frequency crystal oscillator stepped down to one Hz. These can be made very frequency stable, especially in the relatively constant temperature environment of a human wrist. Drift is much less of a concern.
Or you can have it all. My inexpensive Casio has an electronic drive and resynchronizes the absolute time by listening to the NBS radio broadcast every night. In addition, the dial face is a solar cell so it has no battery; a capacitor stores charge when light is available.

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