STID is NOT cerebral, but it is topical. It's more relevant than 90% of the ST movies.
Here's an incomplete list off the top of my head. You may disagree.
'The Cage' thinking issues:
1. The morality of Pike perhaps not answering a distress call.
2. Pike's disaffection with being in command and being in control over so many people's lives.
3. How people would cope with not being able to trust their eyes and ears.
4. Would being trapped in a 'Cage' where all your wants seem to be satisfied be that bad?
5. What about the fate of Vina?
6. Would you really kill yourself to avoid being imprisoned in a guilded cage for the rest of your life.
7. What about the fate of the Talosians. Surely Starfleet could help them is some way. But was it worth the risk?
8. A woman as 2nd in command. The horror of it all.
STID 'thinking' Issues.
1. Is it moral to execute an enemy of the state without trial?
2. Is it moral to use someone against their will for the greater benefit of your umm planet/country?
3. Was Kirk and co really wrong when they broke the PD?
4. Was Marcus completely wrong in every way? Surely someone had to do something about defending the Federation?
5. Was Kirk too reckless for command?
6. Is it OK for you to invade someone else's planet for a really good reason? And then kill a whole lot of their people?
7. Would you kill 42 people to save your daughter's life?
8. Did they do the 'right' thing in the end be refreezing Khan? What about his followers. They didn't do anything? Yet?
The thinking issues in 'Cage' seem to me to be more 'cerebral' and sci-fi themes while the STID issues are more contemporary political ones - which frankly is what Star Trek is quite often about.