Oblivion, Fallout 3, and Fallout New Vegas could use a 64-bit version. Even if they change absolutely nothing else about those games, that alone would be a major improvement, as they are very prone to crashing from running out of address space, especially if you have graphics mods installed.
Not saying that these shouldn't have a more stable official release, but hasn't this been solved by mods for a long while now? At least New Vegas I remember when I last set up mods installing a fix for this, it's actually quite stable now if you install all the recommended fixes.
No. This is impossible to solve with mods, even those that modify the executable. The entire executable must be recompiled, and the source code likely modified, to make it 64-bit.
You're thinking of the “large address aware” flag. By default, Windows doesn't allow 32-bit programs to use all 32 bits of memory addresses, because some older 32-bit programs don't work correctly if they encounter a fully-32-bit memory address. A 32-bit program must be specifically marked “large address aware” to indicate that it will still work correctly if it sees fully-32-bit memory addresses, and only then will Windows allow it to use all 32 address bits.
The mod you're thinking of simply sets the “large address aware” flag on the Oblivion/F3/FNV executable. This works because these executables are in fact large address aware; they just aren't marked as such because of an oversight.
That helps, but not much. It only extends the maximum memory that can be allocated in Oblivion/F3/FNV from 2GB to 4GB. A 64-bit Windows program, like Skyrim SE or Fallout 4, can use up to 131072GB of memory, and that limit will increase even further in the future.
Needless to say, these 64-bit games, unlike their 32-bit predecessors, will not crash merely due to running out of address space. That was a major source of crashes in the 32-bit games, so this makes the 64-bit games significantly more stable.
Also there is a modding team making a remaster of new vegas using the fallout 4 engine. It looks really impressive, they've been working on it for years now.