Biodiversity requires incremental, organic evolution. Funny how humans think that our intellect can somehow solve every problem.
This is better than nothing. But species don't exist in a vacuum. Re-introducing an extinct species to a biome could be as jarring to its neighbors as its original elimination was. The most conservative path would be to cauterize the would and let the system heal, even if it takes a few million years.
For an absurd example, consider the effect of introducing a large number of saber-toothed tigers to their original habitats.
Life is a process, not a state.
While you are correct that evolution would sooner or later take over, whether with assistance via cloning or blind luck if humans were to go extinct, you do need to consider the possibility that under some circumstances systems can collapse rather than bouncing back over a relatively short timeframe. Life would eventually re-establish itself, just as life persists in extremely arid desert conditions, but there's no guarantee it will do si n a timely fashion, and by timely here I mean on a timescale short enough for a human civilization to flourish in parallel with it.
There isn't a stable state, but there are multiple equilibria. We can quantify the robustness of an ecosystem, its resilience to exogenous shocks. That makes certain states "better" than others.
That resilience is low and decreasing. "Healing" means helping it increase. Re-introducing extinct species may or may not build a more robust and more productive biosphere.
Besides that, most people in cities already live in a biodiversity wasteland.
Okay fine, that very well be the case, but I think most of us would prefer not to live or have children or grandchildren that live to suffer (and probably be one of the casualties of) a 99% or higher percent population decline, which would still be 76 million people at the current population count.