Yes, most effective construction decks are keywordless and most effective keywordless decks are construction.
It would be really cool if we got one or two keywords that focused more on construction than destruction (or resources), and cards that made keywordless attack more viable.
You could argue that Unliving is construction-focused, but back when I played an unliving deck, I'd say I won less than 50% of my games by construction. Lots of destruction victory by Water Elemental/Colossus/Genbu and a fair few resource victories from +quarry and unliving keyword effect.
could be the keyword you are looking for.
We still have to fully develop it, but I think that if we create some synergies with unliving
it could become a good tower oriented keyword.
For sheat your sword I simply suggest to raise its cost (4/4/4 ?)