In a healthy ecosystem, everything has a purpose - the thistles and brambles cover the bare soil and prevent it blowing it away, animals cannot eat them down (though goats give it their best shot), their roots go deep and bring minerals to the surface that have been diminished. The so-called weeds are the soil's rebuilders, the guardians and protectors of our biota in any area.
Where mankind interferes (and sometimes nature interferes, in the cases of wildfire), the balance is temporarily disrupted. When we spray for one species, or dig it out or burn it out, all we're doing ruining the balances. Nature will fill those gaps as fast as she can with whatever she can and in that way, the soils are worsened. Grazing animals choose the most palatable food, and if they're confined to a small area for too long, there will only be unpalatable plants left - the animals, needing nourishment, will dig until they've eaten all the roots of the more tasty plants. But rest that soil, remove the animals for a time and wait and the palatable plants will return - and outgrow the weeds, and the weeds will gracefully retire, until needed again.
We lived with agriculture very well when we fed ourselves locally, the cycle of resting and replenishing nutrients and minerals established.
Trees (and other plants) that are considered invasive have strong survival and reproductive mechanisms, essential in their home territories. But in a gentler landscape and climate, they can overrun the local flora with ease. Choosing garden plants with some intelligence as to what they require and where they came from is usually a sufficient safeguard. However, too many are more interested in rarity, appearance and staying ahead of the Joneses to exhibit the needed intelligence.