There's plenty of appetite for opening back up, which'll almost certainly bump up the curve. No one's saying outright "let's have more infections!", but it'll be the end result of the reopening policies.
I am not sure that it is the policy. In the US or Europe, all governments have warned that they would back down from opening up if they see a rise in new cases.
Sure, they're going to have to ride the rollercoaster up and down for a while. I suspect we'll absolutely see further lockdowns; the question is going to be how long we can go before declaring one.
More data is good for determining how far we can let things grow before locking down, but it's confounded a bit by social factors like people getting tired of the bumpy ride and not following them as well after a while.
Even hard-hit NY is looking to do it fairly soon; most of our regions just need more tests and contract tracers hired. https://www.governor.ny.gov/programs/new-york-forward