I can't find information about right pronunciation of patchim ㄷ(ㅅ, ㅆ, ㅈ, ㅉ, ㅌ, ㅊ) before ㄱ. From what I can hear ㄷ should be silent. But I am not sure about it.
For example in words like 웃겨 I hear 우껴 and not 욷껴. Similarly 맛있게 for me sounds like 맛이께 and not 맛읻께. The same with 맛있겠다 which sounds like 맛이껟따.
Sample audio clips:
For 맛있겠다 https://forvo.com/word/%EB%A7%9B%EC%9E%88%EA%B2%A0%EB%8B%A4/#ko
For 맛있게 https://forvo.com/word/%EB%A7%9B%EC%9E%88%EA%B2%8C/#ko
I agree with you; in regular speech, the 받침 is skipped over in words like 웃기다 and 맛있게. Wikipedia:
When plain stops /p t k/ are not followed by a vowel, they are not released [p̚ t̚ k̚].
The unreleased /t̚/ leaves the tongue in a position that makes it very uncomfortable to make the /k͈/ that follows. Try pronouncing the word "wildcat" without releasing the d, as if it's a Korean 받침. It almost feels like you're swallowing your own tongue, not a pleasant experience. After /t̚/, the tongue is firmly planted on the alveolar ridge while holding in an unreleased breath, obstructing the tract. To make the /k͈/ from there, you would have to drag the tongue back to the velum without releasing at any point. Not pleasant.
The huge majority of "exceptions" in Korean pronunciation (and many other languages) are for these reasons; in fact, the ㄱ becoming ㄲ is an example in itself.
I don't know any Korean. However, I have read about it, and the thing that you mention hearing is listed as a feature of Korean pronunciation in A Reference Grammar of Korean, by Samuel E. Martin, page 31.
Martin says that ㄷ+ㄱ that is originally across two syllables ends up being turned into ᄁ, a tense consonant at the start of one syllable (and that /t/ is likewise lost before other tense consonants, including ones that became tense because of coming after a consonant, or before aspirated consonants). However, I think that this is an optional part of fast speech, so that you could also hear a [t] sound before it sometimes.
Actually, something a bit similar is supposed to happen in English: supposedly, /t/, /d/ and /n/ in English can assimilate in place to a following consonant, making "good book" sound like "goob book", "bad cold" sound like "bag cold", and "ten piles" sound like "tem piles". But this is not something that English speakers generally notice or think is happening (and I've read that even if it is hard to hear, the tongue position might still include the original position of /t/, /d/ and /n/), so it wouldn't necessarily be recommended for an English learner to make a special effort to try to pronounce things this way. But it can help to know this kind of thing so that you don't get confused when listening.
