It makes the game more interesting.

I agree. I often wonder what the order is of the cards that come up in the next phase so I can better determine the effects of previous actions. Perhaps there's a way to first show the order that the cards came up in when beginning the new phase, and then provide a button where the player could autosort the cards by value when they are ready to do so?

Yes, I think cards should be placed on the board in the order they were drawn.

In this game, mistress on the 1st round is very important.
In my opinion, arist 4th starter should not flip 4th arist.
If flipped cards are placed on the board in the order, we can know who caused to flip mistress.
On the other situation, we sometimes take the meaningless card to flip more UG cards.
If flipped cards are placed on the board in the order, we can know whether the playing worked.
If flipped cards are placed on the board in the order, the game becomes more interesting.
If real play, we can know it.

the reason why take meaningless card to flip more UG cards, to flip UG arist.
it sometimes happens at the last round.

it is a problem that we can't know the information that we can know at the real game.

As debjwillis writes, one benefit of knowing the order of cards drawn is to ascertain the effects of previous actions. If one, for example, purchases or reserves a card in a given phase, one more card is drawn in the next phase—/which/ card, however, remains a mystery in the current implementation because the cards are automatically sorted. But if the cards were instead shown in the order drawn, the "extra" card would be obvious.

I've upvoted this suggestion, but I think that it should be implemented as a player's preference, with the default setting corresponding to the way the game currently operates, so as to provide no disruption to all players who are used to the current functionality.

Alternatively, if the log were to indicate which cards are drawn—one card per log entry in the order drawn—I think that that would be an acceptable alternative to implementing a player's preference.

It's an interesting suggestion, but it reminds me of "chasing the rabbit" in hold em poker. While it's interesting to see if your choice was the correct one, it won't (or shouldn't) change your mind about that prior choice. Beyond self-validation, it doesn't really add anything to the game or your strategy.