I thought I had replied to this discussion earlier, but don't see it ... it's entirely possible my pregnant brain meant to post, but never actually did!
My husband is a former mountain bike racer, and now races duathlons (running/cycling) races. He went to the national championships for duathlon as an amateur racer, so he's definitely in the 'confident rider' category.
He won't even bike with a bike seat on the bike. Trailer, or no kids. Nothing to throw off the center of gravity & balance ... it's not worth the risk to us at all. Bike trailers are available at every price point, and although we got a very nice one (DH used to race for a bike supplier, so we got a great deal on it), there are loads available used in our local classifieds all the time, and they are safe for both the adult cyclist and the child.
Regardless of how good a rider a person is, it's like carseats ... you can't count on everyone around you to be safe as well -- if you have to make a quick action on the bike to avoid the consequences of someone else's bad choice (drivers not giving bikes enough space, dogs & children darting out on quiet country roads ... dogs chasing bikes ...) you need to be able to make that action without having to think 'how can I do this and STILL balance junior on my back', or having their weight slow your reactions/balance.
Trailers increase your 'size' as a cyclist & make you easier to see, and they all come with those orange flags for safety, making you even more visible to cars, which only increases your safety.
It is a choice only you as a parent can make, but I think it's valid to consider all the angles, and know that even most very experienced cyclists who race would not do it. I can't think of a single parent that races with DH that would even try it. I think often recreational riders (and recreational paddlers, runners, swimmers etc) ... don't see the full big picture, b/c what they do is always 'fun', it's not competitive. Once you get to a competitive level, you consider every little detail and are more aware of yourself, your true abilities & your equipment. Not to say that competitive riders don't take risks, but they consider the risks differently than a recreational participant might.