I don't want to rain on anybody's parade, But Strapping a passenger (Kid or other wise) to the bike or the rider is asking for a possible terrible thing to happen.
Given the various likelihoods of problem this is a trade I'll make. The kid is not strapped to the bike. She did that when she was tiny and all we did was ride around the field or park. No other traffic involved and not on the street.
Once she got big enough to know to generally stay put, however, the far more likely concern became her dozing off or lack of long term attention span leading to her leaning too far. Hell, even a good solid pot hole might bounce a little one off.
Yes, if we ever laid it down her and I coming off together might open up potentials for injury involving contact with me that might otherwise not occur. Or I might control the slide more than she would and she might be better off. That one seems a toss up.
That of course is the worst case scenario. It is readily accepted such a thing could happen. It is far less likely to happen, however, than her falling asleep and flopping over, falling over if I just accidentally drop it to the crash bars, or her just doing something a wee child might always do and flop around on her own. With the harness we've used I choose to protect against the far more likely rather than the lesser likely cause of potential harm. Admittedly, it is playing the odds. That doesn't always work. But it's the best I can do.