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Generally, something like Dropbox and LaTeX work fine - unless you have two people editing the same file at the same time. Then, any VCS or something like Dropbox fail miserably. I have tried https://www.writelatex.com/, but of course I'd like to keep using my local Aquamacs instead of a web-based solution. Maybe I'll write a synchronization tool for Emacs. The issue is then that we need to integrate people who don't use Emacs...

https://www.writelatex.com/ and https://www.sharelatex.com/ and several desktop latex editors seems to work OK despite your logic.

The main appleal of LaTeX is precisely that you aren't supposed to continuously re-render it, you are supposed to write things. Then you twiddle how it looks a bit at the end.

Optimizing web pages for speed of rendering the output seems reasonable, but I'm not sure that should be a big consideration in a document format.

At writeLaTeX.com, we compile automatically, typically every 5s-10s. One of the things that makes it work is that the server can cache most of the stuff that doesn't change often, such as the figures. This does require a bit more sophistication on the client end than just uploading all the inputs for every compile, but it's definitely possible. In terms of packages, we run a full TeXLive distribution on the back end, which covers most things. (But we still have to install CTAN packages on request from time to time.)

It's all about workflow, Once you have some bibliography files, an editor you know how to use, a few tools you can trust for making graphics in the right formats (I have to admit to using ... xFig) then LaTeX is fast and easy and far more cross-platform than a word processor. For papers in physics and maths, LaTeX is a winner. But it has the learning curve issue. Now and again I _have_ to write a paper in a word processor for a conference that will not handle LaTeX and it drives me mad. If you don't like embedding pictures in LaTeX, then you must have doing it in word, What are they anchored to? If you try to copy and paste, which properties come with the image, which don't? Half the time if you try to drag an image word sits the image off the bottom off the page or makes it go invisible. Open Office is even worse, half the time you can;t tell if it is linking to a file or embedding it and they just vanish leaving big red X everywhere. And if you've never tried it, I suggest https://www.writelatex.com/

Additionally, there are multiple online latex editors (eg, https://www.writelatex.com) if you want to be clouded.