The signal is not 60 kHz wide. It is at 60 kHz. A pure carrier with no modulation has the inverse of infinite bandwidth. (Assuming perfect transmitters, which can't really exist, of course.) The faster you modulate the signal, the more it spreads out across the spectrum. The frequency-time tradeoff.
The time signals run at the low end of longwave. That spans from about 40 to 120 kHz or so. There is about 100 kHz of spectrum down there. Though broadcasting a broadband longwave signal like that would be an imposing task. To cover a large area with AM broadcast (maybe 5 - 10 kHz) uses 1 - 2 megawatt transmitters in Europe. To cover the continent with a 100 kHz broadband digital signal would probably take 10 - 50 megawatts, maybe with 3 transmitter sites. Though I think it could be done. Could fit maybe a megabit a sec in there.
Something less ambitious maybe. A few hundred bytes a second? A kilohertz or so of spectrum used. It could work inside elevators, deep underground in parking garages, and so on. Digital alert stream for emergencies, time signal, etc.? Would not be much more complicated than the time signal transmitters, just with a more sophisticated modulation.