I dunno if a "cheap drone" can produce the same magnetic response that a fucking cargo ship can, but it seems extremely unlikely.

And what, you have 2 in the water ahead of you? Is that enough for it to be clear for a cargo ship? They function perfectly all the time and catch every single mine?
What happens when 1 finds a mine? How many extras do you carry? What happens when you run out, "just turn around"?

Drones could probably clear a shipping channel, but at some point and actual ship is going to have to go through it.
And the suez canal was blocked for ages due to 1 ship, even after having been operated for decades. That, except the ship sinks.