....at some point they'd be on a collision course.
I hate to disillusion anyone but with many go-around procedures ATC must act pretty quick to resolve a future conflict - that's just a fact of life with current traffic levels.
But, hey, if you want to carry on thinking up disaster scenarios that are incredibly unlikely to arise in the real world please feel free (but I'd prefer it if you did it on your own time). I guess you must be a reporter or TV producer....