In the case of “hadn’t” – the sounds are not dropped. Can you hear speakers dropping the sounds in your head every time? If so then why? If you can talk to “dinnit” instead of “didn’t it”, you automatically get the word “dinnit”. Native speakers sometimes use sloppiness like this.

TV and radio commentator usage attempts to not use accented or regional use. Normally a Spanish version of the most commonly accepted English word is used by most people. Wet usage would pronounce the “‘N” and the “d” respectively.

The d-n consonant combination is mechanically difficult to reproduce, and there are regional variations in dealing with this. In some accents, notably those where speech is rapid, the d is shortened to a gluttal stop “ha’nt” or even omitted altogether “hant.” What is the proper pronunciation for Wales and the Marches. In places where the pace of life is a bit slower- Wales and the Marches, for example- the problem is eliminated by adding a schwa between the d and the n so it is pronounced “had a nt”, with the d clearly enunciated. As in the Goldilocks story, the Received Pronunciation version is not too much, not too little, but just right.

The position of the d is changed and the d is softened. The d is not dropped. The plosive of the regular d is made with the tongue on the gums, releasing air through the teeth. With the Dn combination in hadn’t the tongue remains against the gums and the soft palate: the plosive occurs using the epiglottis, allowing air to pass through the nose.

I can’t find a recording of hadn’t, but here is one of didn’t.