.....You want decently made luggage that isn't going to fall apart. But I see plenty of people (not me) using unwheeled duffels - they do tend to start lighter without all the structure/wheels/handles sucking up your weight allowance, not to mention less expensive. If by "sturdy" you mean hard-sided, that's definitely not a requirement. Most scuba gear is pretty sturdy and will be perfectly fine in a carefully packed softside bag. People do it all the time. (I have for over 20 years.)
Occasionally a liveaboard will have a place to store luggage on shore as you experienced, but usually they are going to store it in a variety of places on the boat. Most boats have all sorts of holds and storage places that aren't obvious until they open them. (Do make sure you remove anything from your luggage you might conceivably want for the duration of the trip, as your luggage could wind up very inaccessible, like in a hold under 20 other bags.) Pretty much any liveaboard will discourage hard luggage - if too many people brought large hard luggage they'd probably have a problem stashing it all. If there are just a couple suitcases like that it seems most are able to manage. But I'd say it's better not to be the person bringing it - borrow something more appropriate if you can, and invest in something if you will do more liveaboards.
Some cabins will actually have enough space to stash at least some of your luggage. We tend to keep at least our carryon bags in the cabin, especially if we have a top unused bunk to put them - they make great extra "drawers" for all your random little stuff.
