What does sharpness being reduced 50% mean? Does that mean with 2x+1.4x relative to bare lens? Since adding a 2xTC can increase resolution by a maximum of x2 and a 1.4xTC by a maximum of x1.4, it doesn't look as if you are gaining anything by stacking them.
You've got a point. But remember the 2x extender increases the pixels on target by 4x. 2x in two dimensions, if that makes sense (so, say the bare lens gave you a subject 1000x1000 pixels, that would be 1MP; doubling the focal length gives you 2000x2000, which is 4MP).
It has a couple of advantages I would say. First, it makes the subject bigger in the viewfinder, which can help if you're focusing manually. Second, if you were to crop to the same size the noise patterns would be different. again it's hard to put into words. But shrinking down an image taken with a longer focal length would reduce the appearance of noise, whereas simply cropping to give the same field of view at a shorter focal length makes the noise more apparent.
In my subjective view, 2x + 1.4x does give extra resolution. Beyond that, you're not gaining any extra details, but the above points hold (the big exception being stacked astrophotography, where you regain all that resolution by combining multiple images, so any extra focal length is good).
In terms of number of pixels, sure doubling f means you get 4x more on target. However, if you halve the the resolution in 1 dimension you lose 2x2 = 4x in two dimensions. So, you have got nowhere. Now mackguyver has just found that adding the 1.4 to the 2x lowers the sharpness from 80 to 50%, ie by a factor of 1.6, for an increase in f of 1.4x. So you have actually moved back in resolution for a loss of autofocus and aperture.
Oh, I think I interpreted '50%' differently. It's definitely something worth testing, I've never done it systematically. If I do, I'll post my results here (as I said above, my subjective impression is it's worth it up to a point).