MOABs can pressure the opponent at most stages of the game, while additionally supplying Bloontonium.
Ignoring additional income, Player 1 can play a MOAB as early as Round 3, while Player 2 requires Round 3. However, on High Finance, Player 2 can play it as early as Round 2.
During early rounds, a single MOAB pressures the opponent to use single-target damage to chip it down. For early rounds, sending one MOAB first and following up with another MOAB helps pile up pressure gradually, while sending two at once should be done if suspecting an early Mortar (especially Burny Stuff Mortar).
MOABs are often paired with BFB to maximize pressure. However, the MOAB is cheaper, allowing it to be played earlier, and generate Bloontonium in factors of 3, but less efficient HP than the BFB.
For Quincy in particular, it is often more reliable than a BFB for efficient Bloontonium. As a factor of 3, two MOABs give exactly enough for full Bloontonium, whereas with the BFB its 7 Gold cost it's more easy for him to overflow on Bloontonium.
Other Bloons in factors of 3, such as Bloontonium Gas Bloon and Yellow Bloon, are effective for precise Bloontonium gains on Heroes whose Bloontonium meters are factors of 3, such as Adora and Gwendolin.