The data share set up in 2012 is a group of linked databases for the police. It has nothing to do with this.
That said, I do agree that a system (whatever it is) is only as good as the data and, the people that run it. However, that isn't the point. The point is that it was a lie to say we aren't allowed to turn away criminals. We are. Whether or not we manage that is a matter of competence, not law.
We are...but there is a 'however' from the 2004 link you posted.
Previous criminal convictions aren’t on their own a valid reason to deport someone.
Public policy or public security decisions to deport someone should be “proportionate”, and based exclusively on the behaviour of the individual involved.
The person’s behaviour must be a “genuine,
present and sufficiently serious threat affecting one of the fundamental interests of society”
In addition too constraints built up by 'length of stay rights....again from the CD link you posted
0-3 months when the UK can refuse individuals entry or deport them for public policy, public security and public health reasons
3 months – 5 years when the UK can deport individuals for public policy and public security reasons
5 years – 10 years when the UK can deport individuals for serious reasons of public policy and public security
10 years plus when the UK can deport individuals for imperative reasons of public security
So what does all of this mean?...again from the link you posted;
Public policy or public security decisions to deport someone should be “proportionate”, and based exclusively on the behaviour of the individual involved
Previous criminal convictions aren’t on their own a valid reason to deport someone
The person’s behaviour must be a “genuine, present and sufficiently serious threat affecting one of the fundamental interests of society”...posted above already but from the the link it's also in the summary.
Countries can’t deport a person just to make an example of them.
Competence only became an issue after the law was introduced to share information....as already stated this was some 8 years after the directive of 2004 came in to use....and from the link you posted I have highlighted the difficulties in refusing entry.