"In other words, if I, as a retail trader, wish to place an order, it must be done at least 1 minute before the close, making it impossible to time it as the last trade of the session."

So then you would plan your trade for the last second of the penultimate minute and achieve the same thing.....but strangely enough I have traded a number of times in the last minute of the day. Did one just the other day.