The fact that it has a price and is only around for a limited time is what's motivating even more people to have it, because there's a reason to get it, else it's gone forever.
As I said before, it's counter-productive to the whole "rarity" crap, because so many people are clambering to get it in time. When "rarity" finally comes into play, it'll be far in the future, when the event has been mostly forgotten, people have gotten rid of the car to make room for something new and more new players have joined.
If it were free and not timed, it'd probably end up in the same position as the Beach Bum stuff. Some people would still get it because it's a classic, but most wouldn't bother because they don't have to. People certainly wouldn't get it for it's performance, which is kind of decent, but nothing to write home about.
The Biffie has decent performance, last time I drove mine. It's a speedy little thing, and yet not many people have it or use it.
It'd be rare, or uncommon... But not in the kind of way people like.
But this is all just assumes, yo.