Bloonsday Device is designed with control decks in mind, and is a counter to midrange and tempo decks if obtained soon enough. Both players have their Bloons completely destroyed, unlike any other board clear, and the most expensive with only one per deck.
In midrange decks, Bloonsday Device can be used to deplete the opponent's tempo, resetting the board so you can begin your own tempo in the next turns. However, avoid using it if your tempo is better than theirs.
As an Ultra Rare, it can be drawn by ULTRA Rare Power, in fact a reliable way to obtain it. If certain that it can be drawn, it's basically 18 Gold to access.
Bloonsday Device can be used to cancel a Red Bloon Apopalypse, to clear space for Storm Bloons, though this is very expensive.
Since OTK decks don't really care about the Bloons they have on the board until they win the game, they are free to use this whenever they like (assuming they don't need 20 Gold next turn).
Combination aggro + OTK decks can use this against tempo and midrange decks to cancel potential counterpushes, buying more time to draw for a bigger combo or perform a final push.
Dreadbloon has a tendency to build up and string constant pushes of high delay Bloons, supported by its 80 card Deck, powerful removal, and Rock Bloons. Moreover, its playstyle disincentivises playing offensive Bloons (except the Eternal, which is fine with Bloonsday Device). Because of this, using a Bloonsday Device will break Dreadbloon's momentum, allowing time to attack with Monkeys or recover from a board-wide Monkey removal.