I've got platforms on my flat-bar road bike too. And my hybrid and my Bridgestone city bike. My feet never slip off of any of them. When I was riding it up hills last week, I never noticed any problem. I have PowerGrips on my hybrid and so when I'm on the backstroke & try to pull up, it does feel like I am applying some upstroke pull. But when I do the same on my platforms, it feels exactly the same. And there is no effect on my speed uphills with or without the PowerGrip straps - even though they do hold my shoes tight to the pedal.

People write that they feel like they have to hold their feet onto the pedals with platforms. I was trying hard to lift my feet off of the pedals, while spinning at around 90 rpm, and was unsuccessful.