It's just not that clear-cut. Last time around, they apparently culled the wrong animal population. Scientists still dispute to this day whether the action effected anything resembling change. The book "Spillover" (highly recommend it) goes into this in excruciating details, but in particular draws attention to the distinction between a host animal and the amplifier animal. In Hendra's case (Australia), it was a bat -> horse -> human -> random survival recurrence. In other outbreaks, it was not very clear what was what and health officials and some scientists tend to jump to conclusion too early.
What might seem like a rising concern is that there's documentation that the new virus may have made two hops between healthy carriers and infected others.
What might seem like a rising concern is that there's documentation that the new virus may have made two hops between healthy carriers and infected others.