(There's a Dutch politician quoted in the article as saying that Dutch women should have more babies... it seemed awfully odd to me. Upon closer investigation, he was talking about cranking up the birth rate from 1.7 to 2.1.)
Removing discouragement is the same overall as adding encouragement.
It may have the same effect, but it something entirely different. For example, would you argue that legalizing the sale of tobacco or alcohol is the same as encouraging people to smoke or drink?
Now, it's true that what you say about it can have a real effect on choices and outcomes, but we don't really know enough to reliably predict what that effect is in the general case, so for practical purposes, I think we're better off assuming that the effects are negligible.
At least in Austria, it pretty much doesn't matter how much your household earns, up to a certain level (it's somewhere around €2300/month net if I remember correctly), as long as you have at least 2 kids. The child benefits plus family tax breaks compensate for low income. The benefits are diminished (not just proportionally) at higher income levels, which basically means there's an incentive for poor people to have kids. Having a kid probably won't reduce your standard of living if it comes with a 50% raise or whatever. One parent dropping from full-time to part time will also have little to zero financial impact at that level.
At higher income levels, none of that is true. The jobs tend to be more demanding, working part time is hardly an option, and daytime childcare is expensive. The €100/month/child or so the government give you won't even get close to covering that.
I don't know if the incentives are working among those with lower income - they have more kids, but for all I know they would have more anyway, but the current setup is useless for encouraging reproduction across the board.