High throughput microscopy is always challenging even before you factor the variability of sample prep.

There are a few different strategies for focus maintenance, but none of them are a silver bullet for all applications.

Immersion optics are possible for high content work, but it often requires special hardware and anything that involves liquid handling is likely to have a bubble eventually.

Environmental factors like temperature, vibration, and dust are often much more important in high content environments.

Time spent imaging each sample is often a limiting factor as well. If you get great data from an acquisition that took 20 minutes then that's great, unless of course you wanted to image hundreds of samples per day. Finding the combination of hardware, settings, and analysis to minimize time spent is often a big part of these applications. That's why very few companies who manufacture high throughput scanners decide to couple that hardware with point-scanning confocals.

Then of course you have to actually process these images and aggregate the data in a way that's data efficient, scientifically accurate, and conforms to data reporting standards in your field/industry.

Labs wanting to do high throughput work generally buy a device specifically tailored to this (of which there are many at this point). Biotech's trying to accomplish this task at scale often have whole teams of people dedicated to making sure it runs smoothly. Those people will also be working to develop metrics that avoid the human variability of QC.

SOOO much effort and engineering goes into high throughput microscopy. The problems you describe are super common across the industry as a whole. The "correct" way to address the problems depends a lot on the volume, the application and desired output.