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Background for anyone who may not know: I, an EU citizen, have the right to enter any EU or Schengen state (in this case Italy) using either a passport or national ID card. It doesn't matter whether I fly from the UK, Turkey or even the US; Italy is Italy and so EU law applies.

The issue at hand: just flew Chisinau-Kyiv-Milan, and, at passport control in Milan, presented my ID card, but once the officer found I had flown from Kyiv, rejected it and demanded a passport, which I didn't have. He also demanded my boarding passes, which I had left on the respective aircraft.

I politely but firmly explained to him that, per the EU freedom of movement directive, I have the right to enter, and that it shouldn't matter to him where I flew from, but I might as well have been talking to the wall.

I was taken into custody for potential deportees where I was held for over an hour, partly involving two officers asking totally irrelevant questions such as whether I had a ticket back home (which I didn't as it was a re-routed flight - I blackrode trains back home) and insisted that, having flown from a non-EU state, I couldn't enter Italy on my ID card.

Eventually, though, I was handed back my ID and let go with no further explanation.

I've already got an email address to send a complaint to.

What I'd like to know is if, besides demanding a proper lecture of the officer at the booth (whose ID number I noted down, which he clearly disliked) and a written apology from the chief officer, I could also demand financial compensation for being (in the end) 2 hours delayed back home because of this event, seeing as I was held for a completely illegitimate reason.

I'd say the chance to get any kind of financial compensation is low. There is no compensation provision in Schengen Borders Code, and I doubt there is one in the Italian national law.

You can pursue the court case against them, but note that even Article 8 gives the border officials leeway:

However, on a non-systematic basis, when carrying out minimum checks
on persons enjoying the right of free movement under Union law, border
guards may consult national and European databases in order to ensure
that such persons do not represent a genuine, present and sufficiently
serious threat to the internal security, public policy, international
relations of the Member States or a threat to the public health.

Note that there is no limitation on how long this "consulting" should take, and - unlike the rest of #2 in Article 8 - it is not required to be "minimal" or "rapid".

And of course they can claim they had suspicion about the validity of your documents - and until the validity is established, they cannot admit you as EU citizen. Here a point could be made that the border guard lacked proper training. But again its unlikely there is a law which would compensate you for having to deal with untrained government servant.