Learn English – A better way to say “too busy to become more productive”

I am looking for a clear way to describe a situation in which someone is genuinely interested in becoming more skilled, but is so overburdened with obligations that they have no time to learn how to resolve them more productively.
It is different than opposition to new things ("old-school", "Luddite"), and different from useless activity ("work for work's sake", "spinning wheels"). The self-defeating nature is more well-intentioned and less ruinous than "hoist with your own petard". EL&U members: any ideas?