Obviously an accessibility problem
Design issue. Taking it.
It may be that *moving* a post is not something that can happen without a mouse, but splitting a thread off certainly can be.
LiquidThreads has been replaced by StructuredDiscussions on all Wikimedia production wikis (except one, which will be done soon). It is no longer under active development or maintenance, so I'm re-classifying all open LQT tasks as "Lowest" priority.