WebDav was something we tried in the past. WebDav however is not like a typical network connection. Basically every single file is a new transaction. Think like a webpage downloading, it opens multiple network connections, one for each file until a limit is reached.
1Password's most widespread data file (AgileKeychain) has a new file for every single data item in your keychain. This meant that syncing was slow due to the nature of the data file.
Also, checking for new updates to items was also difficult because we had to download every file.
Our new data format is much smaller (file number wise) so webdav may be possible in the future. No promises but I'll definitely mention it to the developers.
The apps that you claim do work with WebDav, likely didn't have the sheer number of files we did. Thus, they worked fine.
Hope that explains in more detail why it didn't work in the past.
1Password 3 for iOS will not work with Dropbox. 1Password 4 for iOS, 1Password for Mac, Windows, Android and Windows Phone will all work fine with Dropbox.
The Sky is not falling
You can read about it here:
http://learn.agilebits.com/1Password4/iOS/Sync/USB/ios-usb-sync-faqs.html
It works well for most people. There are bugs though thus, still beta.
We aren't happy to let it break. The issue is that Apple does not allow us to upgrade applications we've removed for sale from the App Store.
Do be aware we are _not_ happy to let it break. But, at some point there is little we can do. We lobbied to have Dropbox continue to support it longer. Unfortunately, they're pulling down that API support on September 1st.
I made a comment at the top of my previous reply here. Please please read that.
USB Sync is an option:
http://learn.agilebits.com/1Password4/iOS/Sync/USB/ios-usb-sync-faqs.html
We've found that the number of people unhappy about wifi sync is pretty small, but very vocal
We hear them loud and clear. We just don't have a good solution for them outside of USB sync at the moment.
Stella does not work for AgileBits. We have users who are quite happy with the application, who tend to be very vocal and try to provide help and answers. Just like any other person on here

Cut him/her a little slack, if you want to yell at someone, please yell at me as I am an employee with AgileBits. Your frustration is better directed at me.
We're working hard to do what we can to bring all platforms on a level playing field. What you're seeing are growing pains. We started as a small Mac only shop. Then grew to iOS, then it expanded. But our platform support has primarily been Mac because that's where our users have been. It's clear things are growing outside of that. We have major updates coming to Android and Windows that will be the first in a series of updates that will hopefully bring feature parity (as best as we can provide, iCloud for example is Mac/iOS only).
We reply to every user on our forum. Khad, our main guy behind the forums takes pride in making sure he replies to everyone. Will the answers always contain valuable information regarding timeframes and fixes? No. We don't do this not to frustrate you but to make sure we aren't promising on something we can't deliver. If we said "yea, it'll be available in the Spring of 2013" and that time slips by, you'd be upset. So, we don't provide time frames until we're ready to provide them. It's out of respect for you that we don't provide time frames. When we provide one it means we've got something in the oven and ready to ship soon. We don't want to mislead. Contrary to your views, we value our users and their opinions pretty greatly. We listen to them, we bring our users concerns and requests to the people who can change things and many of those changes came in 1Password 4. Sure, we made a few users upset along the way by removing things but we felt we had pretty good reason to do so. We never say never though, so if enough users tell us they want something we'll seriously look at it.
If you'd like to discuss your concerns in more detail please email us, link in my signature, and mention me. Someone will make sure it gets to me and I'll be happy to discuss your concerns and answer any questions you have. Perhaps you may even get into the Android beta if you want. But, that's your choice.

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Thanks for the feedback about usb sync!
We have only charged for 2 upgrades in our entire history.
* 1Password 3 for Mac
* 1Password 4 for iOS
All other versions were free upgrades to existing users. So, a user who purchased version 1 of 1Password for Mac got version 2 for free.
All users who purchased 1Password for iOS (the original version) got 1Password 2 and 3 for iOS for free.
1Password 4 for iOS was the second upgrade we ever charged for. Likewise, many other companies charge for every upgrade. We haven't.
As for what did 1Password 4 for iOS bring?
* Favorites
* Folders (something iOS didn't have but Mac/Win did)
* Browser with tabs (previous version had no tabs)
* Browser fills credit cards, identities, and usernames/passwords (previous version did logins only)
* iCloud Syncing (raving requests for this since iCloud was announced)
* Attachment viewing (no attachment support in previous versions)
* Automatic Clipboard Clearing (just like the Mac!
* Custom Sections and Fields within our existing Categories (you can now add your own data to our existing templates!)
* Many many more
1Password 4 for Mac brings all of the above and many more. I think most users will see it and realize why it has taken awhile to see the light of day. It's been a long hard road for our developers. Believe it or not, iOS was primarily written by 2 guys. The Mac version has primarily been written by 3. Both of these updates are ground up rewrites. From scratch. It was a brand new envisioning of 1Password.
We have much more planned too.