Yes, I think they do that in England. A reported positive LFT counts as a positive test provisionally, and is then either removed if the PCR came back negative or confirmed if it was positive (don't know what happens if a pcr never shows up). Though I think test and trace only kicked in once the PCR was in. But now test and trace will get involved once the lft is reported instead.
I can't see why Scotland didn't do the same... but you're right in that LFTs haven't been counted here at all. They'll probably need to tweak the systems here to allow for it, but I wouldn't have thought it would be that tricky (though I suppose technology/ stats haven't necessarily been PHSs forte til now). I think the reason they said they didn't count LFTs previously was to do with double counting, but now if that's the "only" count of a particular case it should simplify matters?
The doubt I have is whether people will register positive LFTs. If they need proof for work/ travel/ claiming isolation payment or whatever then yes, they probably would, but if just to avoid passing covid to relatives I can't see why people would register it and get test and protect down their neck, rather than just lie low for a bit. Conversely I suppose people fancying a week off work or a gentle week wfh could just register a positive lft without the hassle of actually contracting the virus!