The reason for this translation is because of the Abhidhammic penchant for fitting everything into nice neat categories. They want to match this set up with the 5 aggregates, so they make nice equivalents. But that misconstrues the point of these dhammas (not the mention the five aggregates).
The set of “seen, heard, thought, and cognized” is at root epistemological. It’s not meant as an overall category of things, but of ways that we come to understand teachings, or gain spiritual insight and purification. That’s why the three senses are omitted, as they are not ways that we typically arrive at understanding of doctrines. Once you add “sensed” to the list, it completely loses the whole point of the thing.
We “see” by way of the actual presence of a teacher, we “hear” what they say, we “think about” what they say, and we “directly know, i.e. cognize” the truth of it through meditation and contemplation. If you look at the various passages that talk about how to arrive at the truth, they always use some variation of this.
It’s been some time since I looked at the research on this point, but if I recall correctly, this was argued in some detail by Jayatilleke.
It’s an Upanishadic set, and is found prominently in passages of Upanishadic influence or style, such as chapters 4 and 5 of the Sutta Nipata. In some such cases, eg. Snp 5.8, we find sīlabbata added to the list. This is of course inexplicable if it is considered as a categorization of sense experience. But sīlabbata was a normal way of obtaining spiritual insight or purification.
This is why we’re told that we have to give up such things:
Ye sīdha diṭṭhaṃ va sutaṃ mutaṃ vā,
Sīlabbataṃ vāpi pahāya sabbaṃ.
Anekarūpampi pahāya sabbaṃ,
Taṇhaṃ pariññāya anāsavāse;
Ahampi te oghatiṇṇāti brūmī
One who has given up all that’s seen, heard, thought,
and also precepts and vows;
who has given up all the many kinds of things,
and has fully understood craving, free of defilements,
I declare that they have crossed the flood.
This doesn’t mean that we don’t see or hear anything. Elsewhere, we’re told that we can’t find freedom without these things. It means that none of these things, in and of themselves, bring freedom. If we’re attached to ideas derived from seeing or hearing, we’re still attached.