First, it is possible to have LR import a JPG image without applying any changes to it. And that can be the default for JPG images. If Sharpening is set to 0 then no added sharpening is done.
Second, I have never seen any need or point in re-importing my exported images. The reason for making an export is because you want to have a version of your image outside of LR, for a particular purpose - and that purpose is by definition one that does not involve being inside LR... or there would have been no need to export at all.
I like to keep a clear separation between my LR library, which is a tool for making prints and exports, vs the prints and exports that it has made. A foot and a footprint may be exactly the same shape, but are quite different in their causality and in their natures.
I also find the distinction between picture sharpening, and process sharpening, useful.
One implied objection - how do you judge output sharpening and resampling since LR does not preview these for you - is very valid. I just doubt that re-importing to LR is the best method or context to do that. The OS's standard image viewer can browse the exported location perfectly fine; or if exported for viewing online I will usually want to check what it looks like in the browser as part of checking things have uploaded OK.
I see output sharpening as something that seldom gets varied image-by-image, once tested to our satisfaction and included into an export preset. Once we have worked out what corrects suitably for the blurring effect inherent in a particular form of output, that can also be relied on to suit other images equally well AFAICT - when they in turn undergo the same output.
We soon gain experience at interpreting the Develop preview (e.g. at 1:1 pixel view) in its own terms. As a picture, a range of various outputs still remain equally possible and the master image is not dedicated to any one of these necessarily.
It is the job of output sharpening IMO, to properly maintain whatever look we have achieved in Develop, through the output process.
@richard: thanks for the detailed reply, yes, it's the quality of the final jpeg output that I'm interested in reviewing before uploading to online sites. Specifically the sharpen in export and whether it's introduced noise into sky areas for example. I'm doing the capture sharpening but sometimes LR is overdoing the export sharpening and other times it's spot on, so it needs checking.
I follow your point about this review being done outside LR, but I think it would be a natural feature - ie, image browsing in general w/o regard to developing, for purposes of checking the final output image.
I changed the export to strip out the camera info and it does work fine now if I export to HD, then sync the folder so it picks up the changes. I just found it strange that LR doesn't have an image browser separate from the whole cataloging and developing stages. But no problem as I've found a way.
@rob, I'm outputing jpeg and I'm also importing jpeg's from some cameras. That's where the problem lies - jpeg sharpening is set by camera info which I'd like to keep in the meta of these output jpegs - but I can do without it, so that solves it.
If it's applying sharpening to imported jpegs, unless you strip camera info, then I think it's a bug (Lr is incorrectly treating them as raws). I'd report it to Adobe:
I suppose the importance of export sharpening depends on how much of it you are applying - on the mix between what you do in Develop and what you do at export time.
In my opinion, it is not workable to rely entirely on the export step. The interaction between sharpening and noise reduction is an important one, and the edge masking and threshold settings available in Develop make that the considerably more capable method. Also if (say) noise in skies is going to be a problem, you may as well discover that while you are still working in an interactive way and have the option to "paint" on further NR in the problem areas or to resolve it more generally.
I will very seldom use any stronger than "low" for export sharpening - and therefore simply don't need to worry that LR is going to have significantly spoiled the image. I can imagine that if one used "high" the outcome would not be so predictable; one would in that case want to judge the result each time, and IMO that would ideally mean giving us a PREVIEW before we finalise the export.
I personally don't see the need to REVIEW external images that are not part of the LR library. It might become confusing seeing some images that you could do things to, and others that you could not. I go to the extent of storing exports in a completely separate set of folders, vs those storing the camera originals and the editing workfiles - the latter a completely automated "black box" setup which LR is effectively in sole charge of. But mileage of course varies, and not only do we each have our own methods, we have our own separate aims as well!