No this just doesn't follow for me, in the early days of DRS I found it just as difficult to cop a ball quite clearly taking a decent chunk out of off stump being given not out as I think I would a ball missing being given out. In any case, while the 2 other points about benefit of the doubt going to batsmen and DRS being simplified from a viewers perspective are fair, I'd argue if that it should either be 100% trust in the technology and doing away with 'umpires call' entirely or 'umpires call' applies to both the outside half of the stump and its immediate vicinity, both ways are fair rather than this system that isn't consistent. My preference being the tennis style 100% confidence in the technology.
Given that you've just said that the Umpire's Call zone is too large (which I agree with), why on earth would you want to
double it's size to make it a full stump-width zone of uncertainty?
At the moment the black box that I've been calling the "strike zone" is the area in which they are
certain that the ball would have hit the stumps and removed the bails. Anything outside that zone and you get some degree of uncertainty -- be it margin of error, too close to call, what if it clips and the bails don't fall, what if this completely ****s up how cricket works, or whatever. If not for the half ball-width requirement, it actually makes perfect sense -- the problems arise when you apply the margin of error twice and get ludicrous scenarios when off stump would have been cartwheeling to fine leg but it's apparently 'too close to call'.
In that regard, the stumps shown on the screen are completely irrelevant to the actual DRS calculations. I mean, the broadcasters could do a McDermott and scale down the stumps slightly to centre the margin of error zone around the edge of the stump, leaving the 'strike zone' and the edge of the Umpire's Call zone exactly where they are now, and it achieves your purpose without doubling it's size. But it makes the actual visual component of DRS crazily confusing -- you have to add lines around the outside of the stumps to denote where the 'Umpire's Call' zone ends, and given that Third Umpires don't seem to be capable of understanding how a video actually works yet, I think the simpler the display looks the better.
The other option is to use the stumps as the stumps -- apply no margin of error/uncertainty factor to them -- but to apply that margin of error to the ball. If, with the ball travelling seam-up on the projection, the
stitching of the ball isn't impacting with the stump you go to Umpire's Call. That gives you a solid 20-25mm leeway (the radius of a cricket ball is about 35mm, the seam area takes up, what, 12mm or so of that?), which is significantly less than the current Umpire's Call factor, but still somewhat larger than the actual Hawkeye margin of error. Half a stump width gives you about 17.5-19mm of leeway, which is why I prefer that method to the ball one -- it's closer to the actual margin of error.
Alright, the dimensions of a set of stumps are 28x9 inches, so 711x229mm
Basically, take the 'strike zone' takes a 8.75-9.5mm zone out of each side (and the top) of the stumps, so you get a functional 'certain' stump size of about 702x220mm -- slightly smaller than an actual set of stumps. The 'Umpire's Call' stumps (i.e. close enough that we're not certain enough to overrule the umpire) would then have a size of 720x229mm, so slightly larger than an actual set of stumps. The real size sits halfway between the strike zone and the margin of error threshold -- so you get your "applied equally" thing.
Now, broadcast graphics.
For the sake of viewing simplicity, scale the on-screen stumps to be the size of the margin of error stumps. Your 'strike zone' sits exactly as it does now in the graphic -- a thin black line running down the middle of the off and leg stumps. That way you can consistently display every margin of error call as "just clipping" in order to simplify it for Average Joe sitting on his couch and, more importantly, the technologically illiterate bloke making the decision in the 3rd Umpires box.
You could also go the other way, and scale the on-screen stumps to the strike zone, so that if it only missed it by that much you get Umpire's Call. But LBWs have generally been made on benefit of the doubt to the batsman, not benefit of the doubt to the bowler, so that option doesn't make as much sense to me.