Sorry but this is possibly the most insane idea I've heard on these boards and as the old joke goes "and that's up against some pretty stiff competition".
Because of their concerns over administrative difficulties of decentralization they decide to shoot everybody with a conflicting opinion? Even the looniest genocidal madmen of history usually had a more rational (evil and unforgivable yes but still more rational) philosophy than that. This has no logic, even twisted logic, to it at all. If the British wanted to prevent independence in 'the colonies' then at the least they'd introduce a couple of other punishments first before just lining everybody up against the wall.
As others have pointed out British policy was contrary to this IOTL, they weren't cartoon villains and I don't think the HRE was held up by Whitehall as a point of comparison worth worrying about.
The halocaust was more sane? I doubt it. The French murdered the Vietnamese with any independence documents. Watch Indochina a people's war in colour. Your right, they would probably introduce policies to reduce the chances of it happening.