The fact that org-mode is tied to Emacs is both its weakness but also its strength. By sitting on the Emacs interpreter, org-mode imposes no limits to what you can achieve. The synergy with other Emacs packages is enormous.
You also forgot to mention one of the coolest features of Org: exporting your documents to whatever format you may want, e.g. html, latex, markdown, odt, reveal.js, - and it's possible to hack the export to fit your needs usually with modest effort. Here's an example of workflow to collaborate with Word users, for example: https://lists.gnu.org/archive/html/emacs-orgmode/2015-06/msg...
And here a recent blog post on exporting org to jupyter notebooks: http://kitchingroup.cheme.cmu.edu/blog/2017/01/21/Exporting-...
Other languages also allow exporting to other formats. I use md-to-pdf all the time, and it works well. Integrating the use of other tools in the export process should be independent of the usage of emacs.
You can. It's a plain text file; Emacs provides a "live" and highly interactive UI for it, but nothing prevents you editing elsewhere and invoking Emacs, in "batch" (i.e. UI-less pure language interpreter) mode if you like, to evaluate, export, or perform whatever other actions on the file. I do this all the time, albeit in an interactive Emacs, with Editorial on my phone and files synced in Dropbox.
There are also libraries in languages other than elisp which provide some export functionality; notably, Github uses org-ruby, I think it's called, to HTMLify org files for web UI rendering.
I've been experimenting toward a modern SQL interaction mode, and an Org buffer makes a brilliant place for output - native handling of tabular data, syntax-highlighted code blocks each with the query that produced a given result, headlines, plenty of place for user-added annotations, built-in export, overall a ton of work that I don't have to do.
Doing an outline for that presentation next week, but need to put it down now, and don't want to forget about it? Schedule a reminder or due date right there in the document and it'll show up in your agenda. No switching over to a reminder app. Want to log time spent on it? Do it right there. In the middle of all that and get a phone call with a new task? You're a hotkey away from recording that info without leaving what you're working on.
For me it's the integration of all things organizational that makes it compelling.
http://www.jstatsoft.org/v46/i03
I've been thinking of starting a project specifically in org-mode for quite a while.
IIUC, what org-mode provides you is:
1. a (markdown-like) lightweight document markup language, with lots of syntax hooks ("#+") for different tools.
2. some (even lighter, i.e., no "#+" required) organization-based syntax hooks. These are the TODO/DONE/... labels (plus the "[ ]" tidbits), the table syntax, the metadata (e.g. AUTHOR). In fact, the idea of adding metadata to a lightweight markup language is very interesting.
3. some "programmy" syntax items, including things like tags, spreadsheet-like tables, properties, etc.
4. the agenda view. This is a horizontal search on multiple .org files to create a work agenda.
5. some emacs functionality related to automatic recognition and operation on some of the syntax items. For example, org-table-align will "Re-align the table and don't move to another field".
There are lots of other features, but nothing that other lightweight markup languages don't/can't have too.
My main concerns are:
1. it is inextricably tied to emacs. AFAICT, only (5) in the previous list is emacs-only. All the other functionalities are related to the markup syntax.
2. I wish the org-mode language was fully markdown compatible (I can barely remember the syntax of one, and now I need to use 2).