I believe the research, but I doubt the ACA slowed down increases due to competition. The studies you linked don't show evidence of it either.
Most people do not get to shop for insurance. Individual market plans are all similarly and eye-wateringly expensive (last I checked). And people getting health coverage through work are lucky if they have even two insurers to choose between.
Therefore I don't see any reason why insurance companies would uniformly lower their "baseline" premiums when given access to more information. If they were all competing for your business like car insurance, homeowner insurance, etc. things would be very different.
My claim is that the rate of increase in healthcare costs decreasing is evidence that there is incentive to offer the lowest price possible (and health insurance premiums are a function of healthcare costs). If there was no incentive to offer lower pricing, then it does not make sense that healthcare costs would have slowed down when the number of people receiving healthcare greatly increased after ACA.
Also, health insurance is not like other insurance, and it is barely insurance at all. Over a lifetime, almost everyone will need healthcare, unlike car insurance and home insurance. Due to ACA's various rules around how health insurance can be priced and who it has to be offered to (everyone), health insurance company is actually a misnomer.
I prefer to use the industry term managed care organization (MCO), as it more accurately encompasses the function of what is colloquially known as a health insurance company. The price for individual market plans (which I assume you mean those on healthcare.gov) and the price for employer sponsored ones where the insurer is the one insuring the risk are all priced similarly, and they are eye wateringly expensive because healthcare is expensive.
Employers also shop around for premiums with various MCOs, they don't just choose one. The self insured employers (who pay for the healthcare themselves and just pay the MCO for access to pricing and administration of the health plan itself. I have never heard of anyone choosing between different MCOs at work, that would defeat the whole purpose and really complicate the non discrimination testing requirements.
Either way, MCOs certainly do have to compete with each other for business, if they're selling insurance plus managed care services or just managed care services. And so they cannot just lower or raise premiums at their whim. Bottom line is they do have an incentive to offer competitive pricing, it is not a high margin business to begin with.
Most people do not get to shop for insurance. Individual market plans are all similarly and eye-wateringly expensive (last I checked). And people getting health coverage through work are lucky if they have even two insurers to choose between.
Therefore I don't see any reason why insurance companies would uniformly lower their "baseline" premiums when given access to more information. If they were all competing for your business like car insurance, homeowner insurance, etc. things would be very different.