I think this is very much worth the read:
http://onlineclimbingcoach.blogspot.de/2010/09/review-vapour-velcros-and-ho...
From personal experience - I've always had two shoes - one crappy baggy shoe that I tend to use on multipitches or quite easy trad. And one very technical one (at the moment it's the Scarpa Instincts VS).
I could probably boulder a similar grade with the baggy shoe, but each move would take that much more strength as I'd be applying pressure on the foot in a much less precise way due to the rounded edge. This in turns tires me out and makes my footwork a little bit sloppy and I use more of the arms.
The ultra technical shoes I've had have been very important for teaching me precise footwork and developing that trust that even if you're clipping from a very bad edge or feature on the wall, your foot will stick.
Additionally, as DM points in the article above, you tend to develop this catlike footplacements in which you place the foot always correctly orientated so that the edge is perfectly orientated for maximum purchase. The downturn and the grippy edge seemed to work wonders in developing that.
Having said that, it's true that there are videos of people doing London Wall in Trainers and people have been putting up very hard sport climbs before the idea of downturn came together, however I view it as advantage to help progress quicker and developer slicker footwork, so why not.
I'd just resole mine after I wear them out for a fraction of the price of a new one.