I have a different opinion. I would think that common sense says to first check out whether it might be a simple and relatively inexpensive matter to simply replace the plastic dome. Maybe the crack is all that's causing the leak.
Maybe there is a framing or flashing problem, which would be a more involved repair, but the truth is that skylight failures are rare. I think its just that our attention is drawn to those that fail. We've all encountered endless hundreds of skylights that don't leak. Installed properly, a skylight is no more likely to leak than valley flashing or a chimney cricket.
The idea of being safe and boarding it over for fear of future leaks seems to me no more reasonable than boarding up your windows because they might someday break and leak.