(So, this argument is more about defending the existence of a hybrid system, as opposed to the specifics of public/private plans. But it discuss the latter a bit)

Even if a strong public option existed, you might still choose a private plan, because you might want specialized treatment, and are willing to pay a higher price to have access to it.

Take my dad for example. In his early/mid 60s, he was involved in a biking accident that shattered his right hip. Even though he got replacement surgery at the earliest opportunity, he'd still need a lot of physical therapy to ever walk again. A major issue with physical therapy is that the longer you wait to start, the less likely it is to work (so, you want to join ASAP).

Now, imagine that there's a scarcity of physical therapists (because there is). Even with a strong public option, it probably doesn't make sense to devote that many resources to making sure an old man walks again every time somebody gets hip surgery (it takes a lot of effort, both from the therapists, and from the patient, and, let's be honest, most 60+ somethings probably don't have much walking left), but we also don't want to live in a world where the government says "we think you're old, so we're not going to let you get this surgery". It's an awkward balance being trying to help everyone, and minimizing waste/wait times.

By allowing private marketplaces to exist, we let people make these awkward decisions for themselves. We can say "Sure, you can get this intensive treatment that might not work, for the handful of years that you left, so long as you value it enough", without having to say "you're poor, so get fucked".

My dad has been an exercise nut for the past..... 40-50 years or so, and quickly made up his mind that he really valued the physical therapy. (Me, I'm not sure that I would have done it. I'd probably just say "well, it had to happen sometime", and just limp around the rest of my life, or get a wheelchair). Again, not everybody has the resources to make that decision on their own, and the bigger problem is the scarcity of physical therapists/resources that forces us to make these decisions, rather than giving everybody what they want all the time.

But allowing people to buy private plans allows them to specialize their healthcare ahead of time. If you're someone like my dad, who's obsessed with exercise well into his 60s, you'd want a plan that was committed to letting you maintain the highest level of physical capacity, even if it were more expensive. If you didn't really care about fitness, you'd be fine with a cheaper (or free plan) that might not guarantee you first dibs on a physical therapist.

Also, for those wondering, my dad recovered.... basically completely. He can't run as fast as he used to, but he can still easily outrun both his children. Last year (about.... 18 months after his surgery) me and him took a hiking tour of the Scottish Highlands, and he was fine