If there were no monarchy, it wouldn’t swing in either direction. People would just vote for the most religious and conservative candidates and keep the system exactly where it was. Saudi society isn’t really suited to liberal democracy at the moment because most people don’t actually want it. The only reason these reforms happened is because someone with enough power was able to push them through despite conservative opposition. Could a future ruler reverse some of it? Sure. But without the monarchy, I don’t think we’d have gotten these reforms at all. I’d rather take the risk of occasional backsliding than guarantee no progress whatsoever.

So.. this version of the Saudi Royal Family is swining this way. Other versions of the royal family have not.

With a monarchy, you don't have 4 year cycles. The leadership lasts much longer than that.

Once the safeguard is in place for long enough that it becomes the norm, it becomes harder to reverse.

There's a LOT of possible problems with a monarchy, but the biggest advantage is much longer leadership cycles reducing the whiplash of policy change.