Is this in jest? Only partially. Remember when there were maybe 3 or 4 shoe models per manufacturer? Now they've managed to segment the market so there's a shoe for almost any purpose you could think of (and some you probably would never have imagined). So I'm pondering the possibilities of a potential marketing niche which has not yet been explored by the shoe companies.
what would be unique about such a shoe? I find that my gait is different when I'm pushing the stroller, usually it shortens my stride length - I don't think I run as efficiently, so maybe something to compensate for that. Traction can be something of an issue in mud or any other slippery conditions (I'm not allowed to mention ice

) - 20lbs of stroller plus 25lbs or so of WeeVee breaking away on a turn takes some wrestling back into line, so maybe a more aggressive tread pattern than usual.
I was also thinking maybe a tie-in with a stroller manufacturer - think Nike BoB or something along those lines.