I hope it doesn't become elitist or politically incorrect for public buildings to have analogue clocks.
They'll just become what they've been for me all my life: Decorative items, possibly of historical interest, that you can tell the time from with a bit of effort.
What I'd actually like to see the death of are digital clocks that aren't backed up by an accurate time source. If you see a random analogue clock (that isn't somewhere like a clocktower or railway station, where you expect effort will be put into making it show the right time) you can reasonably assume that it's either some antique mechanical thing that's drifted up to a few minutes since it was last given some loving attention, or it's a cheap shitty quartz oscillator that nobody's touched since the last daylight savings change, and therefore not to be trusted.
Digital clocks, on the other hand, have no excuse. Unless you've got a very good reason to have a free-running clock (eg. a wristwatch or bike computer), either sync them to a time source (GPS, radio time signal, NTP, GSM, the grid frequency, whatever) or don't bother. My microwave doesn't need a clock, and it needs one that's perpetually 5 minutes out even less.