I suspect the reason is due to security concerns about running JIT executable code in 3rd-party apps. I have a harder time understanding full-screen web apps, however. Those should be running within some kind of full-screen Mobile Safari mode.
In general I believe its good to not allow random bits of memory to become executable as it can easily introduce a large number of security and memory overflow vulnerabilities.
Perhaps as part of iOS 4.3, Apple has allowed Safari to circumvent this restriction but not any other application. Which would make sense because they control and are responsible for Safari, but to allow any application to circumvent this restriction could open iOS up to large security issues.
Given Safari is the biggest attack surface and regularly falls prey to exploits they should also disable the JIT for Safari. (Most iOS exploits like the Pwn2Own ones, and jailbreakme.com ones are due to bugs in Safari.)
A JIT works by compiling some chunk of code into a section of executable memory, then jumping to that location. As I understand it, iOS hasn't previously allowed execution of code from "data memory" (various people were curious about this very thing when it was announced they were shipping a JIT). Presumably, the Safari process has some special flag that allows it to write to executable memory, but most other processes do not. My guess is that someone forgot to add this flag to whatever application handles "full screen" pages, although maybe there is a legitimate reason for this.
Edit:
An example of the curiosity I mentioned: http://twitter.com/mraleph/status/43030240175468544
Perhaps you just meant the UI/web process separation itself, but it's interesting to note that Apple is going for a more general-purpose solution.
Benign explanation: some bug in safari
Tin foil hat explanation: Apple doesn't want web apps to be as good as native apps. This explanation kind of falls apart when you ask why they would bother boosting the js engine at all.