If plants transmit the lead to those who eat them how can it also accumulate in the soil? The plants would bioremediate the soil.

It's not 100%. Suppose a plant absorbs 5% of the lead. Well in the first year you get 5% of the lead in all water used for irrigation. But, 95% is left in the soil. Next year you get 5% of 195%. Until, the soil has 20 years worth of lead and all new lead added in a year ends up in the plant. Drop that to 1% and it would take ~100 years to get the same effect.

Note, you would really get a differential equation with several terms, but more or less the same idea just after more time and balanced with water that overflows the field etc.

Ah, yes, of course. I guess at some point you're supposed to develop soil testing and stop putting the toxins in to the soil. And the air. And the water. It's not looking too good is it.