Is there any practical effect to bowing a non-character card (such as a stronghold or attachment) that wouldn't also be a result of playing the triggered ability that requires bowing? Since abilities can normally only be used once per round, and cards are readied after the last action window for the round, it seems to me that bowing doesn't have any real effect.

The only real consequence is that it can't then be bowed to pay costs. For example, if you have a Daimyo's Favor and your opponent bows it, you can't use it to reduce a cost of a card in your hand. Similarly, if you have a Niten Adept with just a daimyo's favor in hand, you can't use the Daimyo's Favor ability to reduce the cost of a card, and then use Daimyo's Favor for Niten Adept.

Granted, in that case you'd just play whatever you have in hand that you were using Daimyo's Favor for, but you see where I'm going with this. It basically stops it from being used for another cost as well. But it does not affect the bonus to skills granted by an attachment, and you can still use the abilities on a bowed attachment. As we see more cards that require you to bow another type of card, it may become a more relevant interaction, but right now it's pretty much corner cases where it matters.

It also opens up future card design.
There could be a hypothetical Event that requires the player to bow their Stronghold as a cost.
That player would then need to decide between using that Event or their Stronghold ability during that round.