There are too many qualificators to go into detail here. You might wish to choose a plant that takes out more of a specific pollutant, or of several. Here are some references for Conyza canadensis specifically, they will give you the general idea why people are interested in this on industrial scale.
Phytoremediation is a developed field, with many plants being screened for efficiency. I would begin with learning what species you do have, and then googling them. (Maybe if you write to some guy who studies something that you have, you can offer him joint research - you gather hay and soil at your place, he analyses them for HM (so you save money). If you have a background in statistics, it raises your chances to Eucalyptus height from about clubmoss height:)
As to ANY difference at all...
The more biomass the plant gains, the more overall quantities of accumulated substances will be taken out (meaning if you weed it out earlier, that will be less effective). Also, if you only mow your lawn, you leave roots in soil, and they will probably contain the highest amounts of heavy metals (and some plants can re-grow later, possibly reaching higher than average concentrations of pollutants). And the part that you have cut off will fly away and add to the general level of pollution. However, if you don't mow your lawn, it might look less tidy:)) there will be status repercussions:))
If the plant is a serious weed, it would likely produce thousands of easily dispersing seeds per specimen (so you shouldn't worry about it NOT appearing again). If there is a wetland in your area, sedimentation processes and typically clonal nature of surrounding vegetation (reeds) will make heavy metals accumulate there (wetlands are sinks), so it is a good thing to take them out from surrounding soil in the form of fast-growing, short-lived biomass. In some (usually rural) areas grass is yearly burned, which would release a significant amount of the collected pollutants into the air (and that is not good).
(And of course, trees will gather pollutants from air more than, say, cabbage does, so if there is any significant effect it should be for vegetables and not fruit.)
So I think there is little to gain from not doing it and at least some good gained from doing it.
So I think there is little to gain from not doing it and at least some good gained from doing it.
There are opportunity costs. It costs time and maybe money for procuring the plant.
Thus spake Eliezer:
It seems that many here might have outlandish ideas for ways of improving our lives. For instance, a recent post advocated installing really bright lights as a way to boost alertness and productivity. We should not adopt such hacks into our dogma until we're pretty sure they work; however, one way of knowing whether a crazy idea works is to try implementing it, and you may have more ideas than you're planning to implement.
So: please post all such lifehack ideas! Even if you haven't tried them, even if they seem unlikely to work. Post them separately, unless some other way would be more appropriate. If you've tried some idea and it hasn't worked, it would be useful to post that too.