You can often see further down the tunnel from an angle close to the tracks than you can standing behind the yellow strip. If someone ahead of you on the platform is already doing this, then they're probably blocking your view down the tunnel, so you have to lean to see past them. It seems pretty silly, but sometimes it's useful, for example, in determining whether the express or local will come first, and you can then switch platforms at the last minute if it makes sense for you.

If countdown timers were reliable and accurate, fewer people would feel compelled to lean out.

More specifically there are two major problems one of which is expensive to solve, and the other is impossible to solve.

The expensive one is providing and making use of lots of sensors so that we can have the best possible evidence on which to base our prediction. Most obviously we need to sense where the train is - the more accurately the better. But it's also valuable to know if the train is moving, and even if the previous platform is full of passengers who will board it before it can leave, or empty.

The estimates may prove wrong because of something as dramatic as a fault, or as trivial as somebody's coat trapped in the door.

London's system has always seemed fine to me, but it's noticeable that buses (for which London also provides countdown clocks) have much poorer accuracy, because as well as the vagaries of passengers they must contend with variable traffic. It only takes one idiot trying to reverse a lorry onto a major street to add 3-4 minutes delay to your bus and of course if you can't see the lorry you have no idea that's where the time went.

I don't agree that it makes sense to reduce the displayed precision as you suggest. The problem isn't with precision, it's accuracy, and you can't really fix that by reducing precision.