Earth is a ball (Oblate spheroid) about 6371 kilometers in radius. It's surface is, therefore about 510,072,000 square kilometers or 510,072,000,000,000 square meters. about 70% of that is sea surface, and not going to be considered (though certainly bio-intelligent trees could probably make use of that, we will leave it aside).
Alice seems pretty tall, but the Vicissitudes are pretty short. Compared to other people who have appeared in the comic, Alice appears to be of unremarkable height. One can assume approximately 1.65 meters plus or minus .1 meters. Alice's reach is thus about 2.7225 meters squared. Alice, however, is human and, therefore, mobile. She can move around. She is not limited to what is within reach of her arms from any one location. Alice, also, is superhuman. It is not unreasonable to suggest that Alice can move faster than a normal human. We know Alice has a pump. We know Alice has a windmill. We can infer, from Alice's speech, that she does not have transportation technology that she uses regularly.
This suggests three possibilities.
Option one. Alice is one of a significant number of witches left by the blink to patrol and protect the earth from the depredations of the space trees.
Option two. Since Alice lacks any reasonable ability to patrol the entire surface of the Earth, we could infer that Alice Grove is the last bastion of human survivors on the planet Earth. While the population is significant enough to prevent a total crash, it is also small enough that a single vector in the form of one person could potentially create an instability that would break its sustainability cycle. Whatever blinked made it clear that the trees could not have the Earth until all of the people on it were dead.
Option three. Insufficient information. Either not enough information to speculate about what's really going on or not enough information was placed in development and the plot makes no sense.
If it's option three, that's pretty run-of-the-mill for Science Fiction. If it's option two, Alice is humanity's last best hope for peace. One would hope that she does not go the way of the Babylon Project. If it's option one, logically the space trees would have sent down more than one Trojan horse.
All of this is predicated upon the fair level of unlikeliness that the Trojan horse would happen to run into a local protector who was specifically hostile to the aims of the trees if said protector was a rare occurrence in a large population. So either the population is not large or of the protectors are not rare.
This has been another mountain manufactured from a garden variety mole hill. Feel free to climb it.
A specific note.
It's certainly possible to someone else's already mentioned this, since I haven't been paying that much attention to all the comments in this thread. However, the Vicissitudes creepy night journey was interrupted when a cloud of nanomachines reached for them. Alice suggested that the nanomachines were reacting to Gavia's nano bots. Alice also said that the cloud is constant, and protects itself from UV radiation by hiding under leaves during the day. So there's no particular reason that that cloud wouldn't be able to find Gavia whenever it pleased.
Alice did not know about Ardent and he is Trojan horse payload. It seems more likely that the now about giant was reaching for him.
The question is, why? The easy answer is to assume that the children's assumption is correct and that the cloud was a threat. A mindless threat that has developed rudimentary distributed intelligence and spends that intelligence gazing wistfully at the moon.
It's also entirely possible that we are not seeing something formed of nano about evolution into a new class of animal life form but a system waiting for instructions. After all nano bots are high-tech. High-tech seems to be the thematic enemy. The thematic enemy lives in space. The nano bots gaze wistfully into space. Ardent is a vector for upgrading technology by touch. The cloud of nano bots is technology and could be waiting for an upgrade.
Assuming that this nano but cloud is a local phenomenon, which it seems to be, upgrading it would be one of the most effective means of distributing an upgrade of vector across a wide area in whatever option scenario exists in the actual Alice Grove plot.
Either way, I think that cloud of nanomachines is more important than simply set dressing for the setting.