I think the intent of the 6.8 Western was to introduce a new 270 cartridge chambered in factory rifles with faster twist barrels that are more geared around shooting high BC heavy for caliber bullets in the 160-170gr range in order to legitimize a factory 270 in to the long range shooting world and do it all in a short action. A 6.8 Western is essentially a 270 SAUM with a 35° shoulder angle.
It was a nice idea but the 7 PRC kind of overshadows it by a good degree. Unfortunately, Hornady's new 7mm came along a few months later with factory ammo and bullets in the same-ish weight and BC but generally shoot a little faster and the ammo cost about twenty dollars a box less.
I don't have a 270 but my dad was a 270 guy forever so I've always kind of had a fondness for them and when Berger came out with their 170gr 270 bullet I briefly considered building a 270 Blaser which would have been a near twin to a necked down 270-7PRC but the idea of building a rifle around only one bullet didn't overly excite me. Now, there are a few high BC heavies in the 270 world but I think if someone wanted a fast twist 270 built I'd go 270 WSM or 270-7PRC to get a little more steam behind those heavy for caliber bullets.
IMO, Winchester has to have about the worst marketing department and business model I've ever seen. They've created and introduced numerous very good cartridges over the years but then they do very little to support them and they just kind of die on the vine. The 270, 7mm, and 300 WSM are all great cartridges but if it weren't for other companies supporting them with their own line of ammo they'd just be another obscure cartridge that could have been but Winchester let die on the vine. Winchester already had the 270 WSM which in my opinion is better suited for slinging the 160-175gr 270 bullets but in their infinite wisdom Winchester thought it'd be a better idea to invent a, smaller, case capacity 270 to shoot heavier bullets with. I mean how popular does anyone think the 6.5 Creedmoor would have been if Hornady introduced the 6.5 PRC, which shoots the exact same bullet as the 6.5 Creed only a fair bit faster, first.