I don't think so. Depends on the center of mass.
Take a look at an AAEGIC cruiser. They appear very top heavy, and in fact had to have some corrections early on. Now, after 30+ years at sea for some of the vessels, they are recognized as very decent sea faring and handling vessels.
Also, look at the Hobart and Daring Classes. They are very similar in appearance and ratios.
OK first big wave is an exaggeration!
THe AGEIS Cruisers had a fine length to beam ratio it was top heavy and at the margins of the underlying hull design the move to VLS alleviated some of the top weight issues by dispensing with the launchers, it didn't have a solid mast and a 10m draught, the follow on Burke's hull was fundamental redesigned with less length but greater beam to improve sea worthiness, but it wasn't perfectly executed and some of the burkes suffered structural issues in rough waters which had to be rectified.
Can't say anything about Hobarts they're not in the water yet as they've had build problems but the Álvaro de Bazán class from which they are derived doesn't have a solid mast either.
The Darings have a huge beam to compensate for it's massive solid mast the length beam ratio of a Daring is more akin to a WW2 era battleship than a modern destroyer.
It might be an optical illusion but that puppy looks like it's long and fine without much draught not something you'd stick a tall solid mast on which will in effect acts as a sail,
But hey they all look the same!