Big things are easier to eradicate, especially if they are slow, unaccustomed to being prey, and nutritious.

Eradicating a bacterium with wild animal reservoir populations (deer, white-footed mice, black-legged ticks, all of which are endemic species) is ... a much harder problem.

Strangely enough, there's even some likelihood that killing off the passenger pigeon actually promoted Borrelia burgdorferi. The passenger pigeon's main food source was tree mast. Large flocks of pigeons would descend and clear the forest floor of food. After it went extinct, the population of small animals which also eat tree mast exploded, and these are reservoir species for Borrelia.

If I could hunt Borrelia with spears it would be over

Borellia bergdorfii does not taste like chicken.

There were far fewer dodos than any given bacteria. You can also see a dodo.