In a completely idealized environment, indeed so. IRL, both American puts and American calls are slightly more expensive than the European counterparts. Besides carry considerations (which are obvious), there are various cases when having an ability to get the underlying early is advantageous such as various corporate actions.
sub-optimal exercise - you mean someone exercising his calls with more time value than the dividend? This definitely can happen, but it doesn't happen too often. The probability of someone exercising the calls that has very little time value and enjoying the dividend is much higher. Assignment by itself is not a big deal - unless is causes a margin call and forces you to liquidate the position at worst possible time. In any case, I just mentioned it as an addition consideration, not a major concern. If I can avoid the assignment risk and do the position with puts only, I don't see a reason not to do it.
You'll see that the put fly is often more costly on microstructure in am-style options with wide-flies close to expiration.