In London, at least, it is a security issue. On 18 Feb 1991, an IRA bomb exploded in a bin in Victoria Station, killing one person and injuring 38. As the Wikipedia article on bombings during the Troubles goes on to note:
Since that time, there have been no litter bins anywhere on the
However, as The Londonist noted in 2011,
Bins Are Back On The Underground [...] A new bid to tidy up the tube
has now seen a 25% increase in the number of rubbish receptacles
available across the network.
It's not clear to me how a 25% increase in nothing at all is helpful, so I'm interpreting this as "bins have been very slowly making their way back onto London's public transport premises, and the rate of deployment has recently increased".
However, I suspect it'll be a while before you can rely on finding a bin on a station platform; probably best to put your rubbish in your pocket, and bin it once you get out on the street.