Audax isn't just a fantasy analogue, it's the real thing.
For me this is a key appeal of audax. It's its own structure, with clear rules and a points system which rewards achievements of long distance cycling.
A Sportive on the other hand (what does that word even mean? "Sport-like"?) is for me a kind of fake event, in which most riders are pretending to be racer-like and "pro". Even the send-off is kind of dishonest with the organizer saying "now this is not a race" while middle-aged men in team kit exchange knowing glances.
Mind you, a sportive is worth riding for glorious moments such as when, on the first climb, the lardy bloke on carbon is overtaken by a young girl with pink handlebar streamers. DAMHIKT.
When I'm asked what the difference between an audax and a sportive is, I say: there's no I in audax.