defending your empire's borders: what do you do?

[Stone Mill]

True, I admit the TDM does better, as you say.

But when you start breaking the AI down, I found that I can constantly replenish minefields, and they will constantly bash ships against them for losses.

In this way, you can whittle them down constantly. Now, in certain areas where the AI comes with decent fleets, the mines will be swept. But that is no reason not to fill 'em right up again after you take care of that fleet. There is no guarantee the next fleet (or ship) will have minesweepers. The AI does not think like a human in this manner.