How would testing everyone eradicate HIV? You'd need to remove the genitals of anyone who tested positive, which I'd imagine would be a little difficult to get through most democratic legislatures.
Seriously, in campaigns to minimise HIV transmission in much of the rich world, they generally use self-interest, people's feelings about their loved ones and the broader sense of social concern as drivers, and above all, non-judgemental honest information - that has worked pretty well in many places (although concern about rapid infection growth in some communities amongst young men-who-have-sex-with-men has been growing recently).
Fear-based campaigning hasn't had a particularly good track record in public health campaigning, at least as far as I recall (just one statistical analysis of road-safety campaigns: http://eprints.qut.edu.au/1839/1/1839.pdf)
Sure, testing everybody in Africa wouldn't get rid of HIV, it would do far more good than just offering them for $1, and it would be a huge step towards eradication - though definitely not the final step.
[Hmm this'll be an interesting one to watch the votes on].