Let me start by saying I am not a "sophisticated investor". Then I'll say I like that the government is trying to protect little old ladies from unscrupulous snake oil salesmen. The basic idea is that people who are millionaires can better manage their money and even if they lose a large chunk they are not likely to see their lifestyle change whereas a little old person who is sold an investment by con artist (pirateat40) salesmen have more to lose.
I do not believe the "average joe" is not sophisticated in the ways of money and I believe he needs protection from snake oil salesmen.
That is the basic mission of the Securities and Exchange Commission. They were formed in response to Charles Ponzi's scheme and the great depression of 1929. They require that anyone offering a public security to non-sophisticated investors is forced to register that security.
The problem is they don't give people who aren't "average joe" or little old ladies any legal way around the cap. If they merely made it harder but not impossible then I would be fine with it. They put a cap, they could have put certification requirements, make people take a college course, but they put a cap. This reduces everyones liberty without providing any reasonable recourse to restore it, without any exemptions, so that the finance professor is in the same boat at the retired little old lady just because of their class.
While I applaud the new program I honestly think hedge funds will manipulate the rules to steal peoples money and just like the Glas-Steagle Act we probably should have left the system alone. Without the cap in place the hedge funds would just take everyone's money. At least with the cap a little old person would need to be ripped off by 20 separate "salesmen" before they can get it all. (Another restriction is that a single investor can hold no more than 5% unless they are a director).
These restrictions are to steal away liberty and nothing else. It's fine to offer recommendations, it's fine to require a license for investors, or a certification, something which can be overcome by studying, or by hard work, or by becoming "sophisticated", but to make "sophisticated" be based entirely on net worth is to corrupt the entire economy to favor rich investors. It's true that rich investors have more to lose so they probably have a buffer, and they might also have more experience investing in most cases, but that doesn't make them any better at investing just because they have more.
Ultimately I don't think the government should tell people what to do with their life savings, their money, etc. The government can make it difficult to lose it all, but a cap isn't just making it difficult, it's dictating what you can and cannot do with your money.
That isn't about protecting people anymore, it's about control. You can protect people by requiring all investors get licensed. This cap is more like putting a cap on the amount of guns or bullets a person can buy and basing it on something like race, gender, age or some other arbitrary criteria. If you invest and lose a lot of money and you were licensed (which means you knew all the risks and got certified) then it's on you. You should be allowed to take risks in this world.