A long answer is available at Islam Q&A, article 40882. In this case, the Qur'an itself provides an explanation:
They ask you about wine and gambling. Say, "In them is great sin and [yet, some] benefit for people. But their sin is greater than their benefit." And they ask you what they should spend. Say, "The excess [beyond needs]." Thus Allah makes clear to you the verses [of revelation] that you might give thought. -- Qur'an 2:219
I guess it's analogous to "Should you run a red light if no cars are coming?". Perhaps it would be safe for careful individuals to run red lights, and one might even argue that running red lights has benefits (e.g. it aids traffic flow). But I feel it's accepted that this is an overall bad idea, as it could result in harm.
What about just a little?
Narrated Jabir ibn Abdullah: If a large amount of anything causes intoxication, a small amount of it is prohibited. (sunnah.com)
If alcohol weren't prohibited in small amounts, it leads to a paradox of the heap: How many drops of alcohol can you consume before it becomes haram?
Also, different people have different tolerances: what's a small amount for one person, is over the top for another. And "one glass of wine" so easily turns into "two glasses of wine", leading to bad decisions.
(Note that alcohol in small amounts indeed affects our mind; see e.g. There is no such thing as a safe level of alcohol consumption.)