Finding things in the sea is basically a question of radar reflectivity and the search area. A ship in the north Atlantic? Its big flat steel sides reflect lots of radar signals, and the search area, while large, is (compared to the pacific and indian oceans) rather small. I don't doubt that anyone looking for this ship would find it fairly quickly.
The problems with MH370 were twofold. One - initially nobody actually knew where it was. The search area was HUGE, and for the first few days there was much less information about the aircraft location. The eventual search area was selected based on quite detailed analysis of the satellite pings the aircraft sent. This took time. It took 9 days for the search to even start in the southern Indian Ocean. Even once they'd figured out roughly where it had gone down, the search area was still astronomically big. Two - aircraft wreckage isn't nearly as reflective to radar as a ship. An aluminium panel floating flat in the ocean will have a very similar reflection profile to the surrounding water.
I think you need a fourth option. Large countries definitely have a technical advantage, but the military still has to obey the laws of physics. Large budgets and no legal restrictions probably put military technology a generation or two ahead of comparable civilian technology - it's better, but it's not magic.
Obviously, you'd need quite some budget to pay an analytics team to find a plane out in the ocean. You can't just conjure the money out of thin air.
And if you go to your superiors and ask them for the money and have to admit it will disclose a lot of your capabilities to foreign powers, you'll likely simply get a resounding "NO". After all, it was never the question of rescuing living people with MH370.
Did you notice how the US kept sat images and phone recordings extremely close to their chest in the case of MH17? I am pretty sure they have a lot more intelligence on that thing than they are willing to admit - they not having constant surveillance over a battle field in Europe would be extremely negligent.
Debris fields are a harder ask distinguishing the debris from MH370 from just the normal trash of the ocean. The ship has the benefit of being a large defined whole and we have a lot of info on other ships' and their location (though the tracking of ships is far from perfect it relies on them keeping their beacon on). It strikes me as a much harder problem to find MH370 because in order to resolve the debris they'd have to take very high res photos so it'd cover a very small area in one shot.
So 2 & 3? They probably used some satellite imagery to look for large chunks but the effort to do the small survey was beyond what they were willing to expend without a better idea of where to search.
Which makes me wonder about MH370.
1. Did a large country find it, but not want to divulge that because it would give away their "find stuff" capability.
2. Did the large countries try, but fail to find it, and obviously not divulge that because it would give away their inability to "find stuff" quickly
3. Did the large countries not even bother looking, because they have more important things to look at.