Do simpler casettes have less issues with missing shifts?
To shift smoothly, you need 5 components to be working together harmoniously: the cassette, the derailleur, the shifter, the frame, and the chain. Any one of those could be causing your problems.

In the specific case of cassettes, there is a wide range of quality and capability in cassettes. Many models have carefully aligned cogs, with little ramps and pins that assist in shifting, whereas others are little more than stamped plate steel. Those differences in quality will dwarf any difference between 8 and 12 speed.

So in short, a high-quality setup at any cassette size should have clean, crisp shifting.

With this said, a new bike should work reasonably well right away. Check that your deraileur is properly aligned, it may simply be a slight bit off and that is enough to cause your troubles.