Many different issues in this one. By way of answer to your question, it seems a bit surprising to try and hang much of this on the controller. Traditionally, the crew operate the aircraft and controllers keep them apart. In the UK some years ago there was a highly misguided (in my view) attempt to involve controllers in responsibility for ensuring that the pilot had calculated an appropriate set of minima in poor wx. I think this is now withdrawn or, at least, watered down to a substantial degree.
That said, the controlling technique appears poor and good practise might suggest that the controller be a bit more aware of a sensible descent profile and ILS interception - but as I get older, I hear myself saying that the young controllers today don't have a good grasp of things like that. On the other hand, they often (and consistently) move more traffic in more challenging circumstances than I faced when I was in ops.
Ultimately, all of us in this business have an interest in not seeing accidents and incidents - and we all have a part to play. And sometimes we might need to step outside our normal mode of operation 'just to be sure' everything is OK - maybe just because the pilot doesn't complain about lousy vectoring doesn't mean it will all be OK.
So I'm ambivalent on much of the main question.
Less so on the recommendation that 'the DGAC study the implementation of a system enabling controllers to determine the vertical position of an aircraft in relation to the published glide path'. What, range from touchdown and mode C aren't enough? Every controller should be able to do the three times table (if that doesn't make sense to you, I do hope you're not an approach controller).
But far more interesting to me is the pitch up to capture the 'false' glidepath. The Dutch Safety Board are looking into a similar incident. There's a
Safety Alert on the topic and an ongoing investigation. Strangely, this is a much abbreviated document compared to the one that was on the site a couple of weeks ago. I am sure there are good reasons for the original document being withdrawn so I won't share it at present but it appeared to be an excellent investigation of what may be a technical issue associated with certain types of glidepath antenna that could result in a pitch up at the wrong moment. I hope that the full report contains all of the information in the original Safety Alert and that it is published as soon as possible.