Sure, people want different facets of themselves on different apps/platforms. But those apps/platforms get bought and sold along with the content and the facet of yourself that you put there.
Ergo, I disagree that we don't have a problem. It's just in a different form and involves the business models both companies and users have become used to (e.g free, ad-supported, etc). For the moment, there are still no viable systems people could move to so they just have to deal with what they get (or disengage).
Self-expression in a particular app doesn't mean that you shouldn't have control over the underlying data you publish, and easily transfer it between apps. Already, many apps such as Tinder ask for your FB account and import your photos. But the import is still limited, and hardly any information is contributed back.
Just like MVC separates data, from views, so too the "apps" should take your data from one place which you control. This place shouldn't be a centralized social network, it should be an open-source server.
In this way, people can upload and manage their own videos, photos, and more. They can then give access to others (friends, etc.) as well as to apps (via OAuth) through their own server. If some of their data streams (e.g. a blog or a video) become popular, then the person pays for more hosting.
The age of centralized services that can go down and present juicy targets to the NSA is temporary. Just like open source systems like git and mercurial disrupted centralized version control systems, so too will the centralized web services eventually be disrupted. The web was originally meant to be decentralized, and it will be again.
Disclaimer: My company, Qbix, has been building the underlying (open source) platform for this exact thing in the last 3 years. And we have had to deal with a lot of issues surrounding identity, privacy, and individual control. Here are some links:
In theory this is true if everyone is being a well-intentioned actor but anonymity can be used to distort a broader agenda into an appealing message; see obscured-funded lobbying campaigns.
Also context is important for whatever one says, and a statement hanging on its own is rarely very convincing. It can be a red flag (whistleblowing) and it can be inspiring (famous quotations) but usually an argument is stronger as a result of the context from which it came (a culture, a person's stature, reputation, etc.).
That all said, I think we need to have anonymity, pseudonymity, and also verified identity. If we choose to share across those boundaries (sharing Facebook details with another service, as an example) then we have to deal with and accept the drawbacks. We can't expect to have isolated identities exactly the way we want them given that that kind of system would be a quagmire for developers to build...
Unfortunately an even larger subset of the population doesn't need anonymity to act nasty to others, while their victims often need it to prevent it escalating. Google's attempts to force real names on Youtube comments to reduce spam and bad behavior have been... less than impressive in effect. In a lot of discussions if you force real names you ensure that those with the most to lose (and often the most at stake) are also the most vulnerable.
Even presuming that counter to actual experience the generic trolls are deterred by a real names policy, there are others who become a much bigger problem when they've got access to real identities. Why do you think doxing is considered such a big thing? SWATing, offline stalking, physical assault, etc. are all risks as soon as a harasser has your info. Even worse when you're talking about something like domestic violence support groups there's a very real danger of the abuser escalating if they discover the victim has been talking to other people. That's 2.1 million people in the US alone who report physical assault by a partner in a single year who could really use access to resources without revealing themselves.
Ergo, I disagree that we don't have a problem. It's just in a different form and involves the business models both companies and users have become used to (e.g free, ad-supported, etc). For the moment, there are still no viable systems people could move to so they just have to deal with what they get (or disengage).