I think it's a function of the way software works: You are trying to design an interface that lets the user do the most with the least amount of effort/clicks. So for each user action, you're going to have more (and more and more) action being performed by the system.
The logical extension is that there will always be more "back-end" programming than "front-end" programming. That's only speaking to domain logic. Add to that things like plumbing and the like and you're even more heavily weighed in on the back-end.
To directly answer your question:
A pretty UI without logic behind it is useless, and fantastic logic with a terrible UI is user-less, so both are absolutely necessary in any successful application, but I don't think that new developers should feel forced to up their design skills and designers shouldn't feel forced to up their programming skills.
People should keep doing whichever they're good at; if that happens to be both, then you're one of the lucky few.
Linkedin do this for their mobile site (see http://engineering.linkedin.com/nodejs/blazing-fast-nodejs-10-performance-tips-linkedin-mobile part 4), and it's apparently been very beneficial for them from a performance standpoint.
However, I'd suggest you avoid doing the same, for various reasons.
The first is maintainability: C#/ASP.net is, due to it being a server-side framework, client-independent, whereas Javascript is not (even with a framework like jQuery you're not going to get 100% cross-browser compatibility, not future-proofing). I'd say it's also easier to verify the functionality of a statically-typed application than an dynamic one, which is something you absolutely must consider if you're building large-scale sites.
The second is that you're going to find it difficult to find other people who are capable (and willing) to build a pure-javascript application of the kind of complexity needed to run your entire website (compared to the relative ease of finding .NET programmers). This might not be a concern of yours directly, but it certainly is something to think about from a long-term perspective.
The third issue is client-compatibility; if you're building public-facing websites then remember that a reasonable portion of the net still does not have JS enabled (for various reasons), so you'll need to be absolutely sure that you're not going to exclude a large portion of your userbase by switching to a JS-driven website.
As for your bulleted concerns:
I wouldn't worry too much about the security aspect, there's no reason why you could not mix paradigms and do some server-side processing when you require security (you're going o have some view-rendering code in there somewhere that returns HTML, there's no reason you can't have this just fire off an AJAX call instead, when required).
Ease of development isn't really a concern too, in my opinion, there are very good tools available for JS development, don't just box yourself into VisualStudio because you're used to it! (try JetBrains WebStorm, for example).
Performance of JS view engines is absolutely fine in most cases (again, in my experience), I use them heavily on a day-to-day basis. What I would suggest is avoiding the more heavyweight frameworks like knockout.js etc., and head instead for something like Jon Resig's micro template engine. This way you can plug in the supporting code in ways you're confident are fast and reliable.
What I'd do, if I were you, is really examine the reasons behind this switch; It could well be that you're just not leveraging .NET effectively and need to up your game, WebForms isn't a particularly slow framework out-of-the-box, so perhaps some of the 3rd-party libraries you're using are slowing down your rendering.
Try doing a performance profile of the application using a load test and profiling tool, and see where your bottlenecks are before you sink a large amount of time and effort into a more radical solution, you'll probably be surprised at what you find as the culprit for your slowness!
Best Answer
The poster boy for HTML5 apps, LinkedIn went native early 2013. In the interview in VentureBeat they explain why.
I think this is the part most relevant to your question:
...