Earlier quoted context omitted.
It would be more than just half productivity. Not only do you have to do the work twice, but you add the delay of someone else replicating before something can be published and built upon by others. If you are developer, imagine how much your productivity would drop going from a 3 minute build to a 1 day build.
Terrible analogy. It might take months to come up with an idea but another should be able to follow your method and implement it much more quickly than it took you to come up with the concept and implement it.
Peer replication is completely unfeasible in experimental fields of science. The current process of peer review is alright, people just need to learn that single papers standing by themselves don't mean too much. The "peer replication" happens over time anyway when others use the same tools, samples, techniques on related problems and find results in agreement with earlier papers.