Step 1: Understanding the Concept:
Banana (Musa spp.) is a giant herbaceous monocotyledonous plant.
Its root system determines its water absorption capacity, anchorage, nutrient uptake, and susceptibility to soil-borne stresses.
Step 2: Detailed Explanation:
Let us evaluate both statements:
Statement I Analysis: Banana does not have a deep taproot system.
As a monocot, it produces adventitious roots from its underground corm.
The majority of these feeder roots are concentrated in the top $30 - 45\text{ cm}$ of the soil profile, making it a shallow-rooted plant rather than a deep-rooted one. Thus, Statement I is incorrect.
Statement II Analysis: Despite being shallow-rooted, the banana plant is highly sensitive to waterlogging, which can cause root rot and wilt diseases.
It also supports a heavy pseudostem and large canopy, which requires strong anchorage and constant water supply.
Therefore, a deep, fertile, well-drained soil (at least $1\text{ meter}$ deep) is highly critical to allow healthy root distribution and prevent water stagnation. Thus, Statement II is correct.
Step 3: Final Answer:
Since Statement I is incorrect and Statement II is correct, the correct choice is (D).