First of all, sorry it took me so long to answer.
And as you are hopefully well aware the basis of free movement within of Schengen is secured exterior borders. That was obviously not the case last year and still isn't in Italy and as such it was obvious to install border controls as long as the exterior borders are not secured properly.
The point is that it is a European problem that got ignored by Europe (as a whole). We have known about this for more than a decade, we have ignored Southern Europe when they asked for help. Merkel, or rather most German parties, deserve their share of blame for not working towards a solution, but I also think it would be delusional to assume that the German public would have been in favor of that. Spending money for a problem that seems far away was never very popular. Offloading the problem to another European country was never a viable solution either though and it has come back to bite us. What you call "open door policy" is a failure of Europe.
I mean right now germany controls the border to austria 24/7 so it's not some crazy fantasy. The difference being that they didn't do it back in 2015 and not in anywhere near the quality of border controls that would have been requried to be able to continue to keep security up.
The idea that the influx of immigrants could have been vetted through border control is fantasy. That is maybe possible for border stops/access points, but not in general. A mere look at German authorities should be sufficient for that. The question therefore (for me) should be how we deal with immigration in general, not whether we can successfully offload the problem e.g. to Italy, which I would like to add would only cause other issues. The truth is that this is a European problem that we have to deal with together. That doesn't mean that one has to be in favor of letting immigrants in, but one should provide a reasonable solution.
Of course the migration streams were already very high in the months before and the people did not just beam there once Merkel made her statement. So good thing I never said that.
My statement happened since you did not intially respond to my challenge and due to the general idea of putting the (sole) blame on Merkel (if not voiced by you, at least voiced by many), the latter of which I find highly problematic. If that was not your intention I apologize.
I purposefully said she signal-boosted the message of "Syrians are welcome here" which led to the increase of fake passes, people thinking germany is now taking in everyone and further encouraging migration movement. As did pictures of people clapping on the train stations to refugees arriving. Pretty much every european politician that isn't from germany agrees nowadays that Merkels statement was a mistake. Even her own sister-party agrees.
I am asking for a quantification on the effects of Merkel's statement and how the situation would look like without that statement. For example, how many immigrants would we have in Europe as a whole and in Germany in particular without her statements (at that time)? I think it is only reasonable to ask someone who criticizes X "What would it look like if X had not happened?" and demand an answer. Not necessarily of you, I know it is probably unreasonable to demand this of common people like us (because it takes a lot of time), but I would expect this of politicians. The reason I am so hung up on this is because we are once again letting populists and liars take over the political discussion, when we should be doing root cause analysis. That happens regarding all sorts of things, not just immigration.
Just to be clear, one can give Merkel blame for a lot of things. I don't think too highly of her, but if I look at the alternatives I shiver.