The "Horror" Of Ben Carson's Health Care Plan

The news headlines today made me aware that Republican presidential candidate Ben Carson has released the "details" of his health care plan. I wanted to know what sort of proposal an actual health care practitioner would put on the table, but I didn't want to get too slanted a view on that plan. So, I made the following decision:

I decided to choose what I thought would be the most hostile (to Ben Carson) source of analysis and, if I could find something positive from that hostile source, I could feel better about the integrity of those positives.

I chose an op-ed in the Huffington Post, and here's what it had to say (in part):

So in place of Obamacare, which includes all sorts of rules about who health insurance companies have to sell policies to (everyone) and what kinds of benefits they have to cover (lots 0f [sic] them), Carson's plan would allow people to open tax-free savings accounts (which they already can) to put away money (which they probably don't have) to pay for medical care until their insurance deductible is met (which it probably won't be).

Set aside the question of repealing Obamacare. I think repealing it would be a good idea, but that's just my opinion.

Aside from repealing Obamacare, is there anything objectionable about letting people set aside tax-free money to spend on future health care expenses? I can think of a few downsides related to demand distortion, but other than that, it seems like a pretty harmless policy.

Why would anyone of any political persuasion object?