Why did Formula 1 need Audi so much that it was prepared to use 1.6l 4 cylinder engines to get them in?

It wasn't just Audi (which is really part of a group that includes Volkswagen, Porsche and Lamborghini too, it could have been an engine badged with any of these companies), but it was new manufacturers in general. F1 needs more manufacturers to provide more competitive racing, the way it is now with 4 manufacturers only is too little. The FIA tried to lure back companies such as BMW and Honda, and new ones such as Audi, with a smaller, cheaper and more efficient engine. However, the costs involved in designing and testing the new engines meant that no company was actually interested (in the end even three out of the four engine manufacturers already in F1 spoke against the idea), led those responsible to scrap the 4-cylinder engines in favour of V6 turbos. Now, whether or not the V6 turbo is better than the current V8 is debatable (even though they cost less and use less energy, they still reach the same top speed with the turbo, and some of F1's greatest battles between Prost, Senna, Mansell and Piquet were fought with V6 turbos in the 80s). One thing's for sure though, V6 turbos are far more suited for F1 than the flat-fours (which are too small even for Touring Cars let alone F1 "the pinnacle of motorsport").