That occurred to me, many buy books from people claiming they died and came back. Its a good business.There is one way where your theory (regarding David being in Hades) becomes possible, IMO, and that is if he was taken there in spirit while still alive, as a way of showing him what his fate might be unless he truly repented. The Lord has done this with a number of people in our time, including many believers who were in some way in jeopardy of going to the wrong place.
That I would find an interesting possibility, but even then there appears to be no corroborating or substantiating evidence, so it could only be presented as a possibility at best, and not used to support your position regarding post-mortem opportunities.
But your argument fails because God didn't flash a scene before David's eyes to teach him a lesson.
David testifies God answered his prayer.
2 O LORD my God, I cried to you for help, and you have healed me.
3 O LORD, you have brought up my soul from Sheol (07585 שְׁאוֹל she'owl); you restored me to life (02421 חָיַה chayah) from among those who go down to the pit (0953 בּוֹר bowr).
4 Sing praises to the LORD, O you his saints, and give thanks to his holy name. (Ps. 30:3-4 ESV)
Think about it. This could have happened in a few minutes while everyone was asleep, so it caused no interruption in his kingly duties.
Also, a literal stint in hell would not be forgotten, and we see David again Praising God for His deliverance from the pit:
1 To the Chief Musician. A Psalm of David.> I waited patiently for the LORD; And He inclined to me, And heard my cry.
2 He also brought me up out of a horrible pit, Out of the miry clay, And set my feet upon a rock, And established my steps.
3 He has put a new song in my mouth-- Praise to our God; Many will see it and fear, And will trust in the LORD. (Ps. 40:1-3 NKJ)