Yea, I've been through some different phases in my life and taken a drug through most of it at the same dosage, there was a year when I had a crazy pricing experience. At the beginning of the year I was covered by Green Mountain Care in VT (the state medicare for all program) and paid 0$ for a 30 day refill of my medication, then I had a lapse in coverage due to employment insurance not kicking in right and ended up paying 264$ for my 30 day supply and when my insurance kicked in I had the Cigna preferred rate of 186$ for 30 days (I had no coverage for that drug, but I did have general pharma coverage). Mid-way through the year we switched insurers and I ended up paying 28$ for a 30 day supply for a few years and then in Nov or Oct a generic came on the market and I dropped down to 3$ of a 30 day supply.
This story is personal and doesn't involve any drugs Shkreli was directly involved with but I'm putting it out there to demonstrate the sort of BS pricing all throughout the pharma market, there are I'm sure some people with bad or no coverage but living just above the Medicaid line that had to pay full out-of-pocket price for Daraprim after the price hike from 13.50/pill to 750/pill, this problem really does hit people.
I agree that there are multiple solutions and issues here, the fact that the government allows market control via eternally extended patents (oh my, read about the history of insulin and how the Canadian inventors released it for free for ethical reasons and now a few companies have a stranglehold on the market) definitely contributes a lot to this situation, but even when looking at medical procedure billing you can easily find crazy market disparities in costs between hospitals down the street from one another - and medical procedures are (mostly) out of the government's hands, that's just unethical companies pumping up the prices on inelastic goods because they can.
Your question doesn't really apply to this last bit but I thought I'd add... Shkreli himself is not just a scapegoat, he was a bad actor and deserves what he's getting, unfortunately it is quite fair to point out that people who have acted equally unethically have felt no problems for their actions because, unfortunately, currently those unethical actions are not illegal in our society - as the Shkreli case and the vitriol around it demonstrates, we, the society, feel like this is an unethical state. There are arguments to be had about the tyranny of the majority and the unfair partial application of the law but... that's all just wool gathering to avoid the truth.