Larry Kotlikoff, who wrote the two 2014 articles that you referenced, uses very strong rhetoric in describing the SIPC: "terrible risk," "financial fraud," and "bigger scam than Madoff." He advises you to "close your brokerage account," and "avoid spending any withdrawals" for six years, presumably the amount of time that the SIPC could confiscate those funds.
This advice is ridiculous, in my opinion.
Contrary to popular belief, the SIPC is not an unlimited source of funds to cover everyone's losses. It is there to address specific circumstances, mainly regarding financial firms that have gone bankrupt. And they also do not generally pay out everything a victim loses immediately. They pay out a portion of it, and then work to recover funds from the crook on behalf of the victim.
From the SIPC's website, the SIPC has a fund worth about $2.5 Billion, and has a line of credit with the Federal Reserve for another $2.5 Billion. In the case of Madoff, however, he had taken in about $19 Billion over the years and had not invested any of it. Much of that money had been taken out over the years by some of his "clients." Of course, his clients thought that there was much more money than that ($65 Billion), because they thought their money was invested and that it had grown over the years. But it was all a lie.
Imagine if the SIPC had simply paid out everything that everyone had thought they had invested, including all of the fake gains? Then Madoff truly would have manifested real money for his clients, and despite the fact that Madoff went to jail, he would have successfully been able to rob billions of dollars for his clients from the public.
Despite the fact that the SIPC did not personally pay back all $19 Billion that the victims had originally invested with Madoff, it turns out that most of them have eventually gotten most of their money back. Some of this money came from the SIPC, some came from Madoff and his partners, but much of this money has come from some of Madoff's victims themselves. Why? Because they had, perhaps unknowingly, profited from Madoff's crimes. They happened to be the ones who got their "profits" out early. So the government has made them pay this money back. This is what was so terrible about what Madoff did.
Kotlikoff has extrapolated this to say that your brokerage account is at risk and that the SIPC will arbitrarily take your money from you at any time they wish. This is ridiculous. The Madoff case is unusual. Steven Harbeck, CEO of SIPC, wrote a response to Kotlikoff at the time that explained the work that the SIPC is doing to get the victims their initial investments back. On the SIPC's website, they still list the Madoff case as an open case.
Even if you have a brokerage account that is a member of SIPC, it is important that you put your money in a broker that is trustworthy. In hindsight, we can see some of the warning signs that were there with Madoff. Victims describe Madoff as having a "reputation as a Wall Street genius." Articles were written skeptical of Madoff's results. It is important to know and understand how your money is invested. Investing in a nebulous fund without understanding what it actually is is risky on many levels, not only because of potential fraud. Go with a broker that you've heard of, and invest in things that you understand. Keep records of what you own, and if your well-known broker does run into financial trouble, the SIPC should be able to help recover your assets.
To answer your example, if you buy actual securities that you understand from a legitimate broker, and they are worth $100K, and they grow, and you sell some of them worth $110K, and the real securities that you still own are worth $120K, if the broker goes under, you would file a claim with the SIPC for the assets that you had with the broker, and they would work to help you recover those assets.