I suspect the reason why UHC has decided to deny so many claims is that this will allow them to marginally lower he price of their premiums relative to their competitors. This'll get them more money via method 1. The whole industry is working around the clock on method #2.
Anyone more informed, feel free to correct me.
From working on automation inside the system at insurers at the time, I can definitively say this spurred health insurers to streamline and lower operational cost overheads.
With regards to the denials, I think you're right too. People like to point at insurers and blame them, but it's easy to forget they're just the middleman.
There's "cost of care" on the other side of them. At the end of the day, premiums need to balance with costs... (somewhat, in aggregate)
There are probably some edge cases where there are opportunities to profit, mostly to do with privately-administered but publicly-funded areas of health insurance (read: FEP and Medicare Advantage), but generally it's trying to get premiums lower for competitive reasons.
Many other aspects of healthcare follow a similar model, where parts are fully private, parts are non-government-but-quite-close-in-function (Ärztekammern and other things) and many to most are public in some sense.
Public system has strictly defined coverage and tightly regulated premiums that are explicitly decoupled from individual health conditions and tied to percentage of salary instead. But providers themselves are decentralized and one is free to choose any provider that complies with all the govt requirements. Private providers can and do exist.
In some cases - e.g. self-employment, or income above a certain threshold - one can opt out of the public system and go fully private. Switching back is then only possible if income drops below the threshold. In practice, 90% of the population is in the public system.