Since the dividend is a known event, why wouldn't the dividend also be reflected in the price of the put (in addition to whatever time premium is left in the put) for the same reason you state above?
I have seen many of my ITM short calls assigned early before ex-dividend. I have never seen a short-put assigned early before ex-dividend. I have read that it is mostly done for tax reasons, but don't recall the explanation.
Yes, pending dividends are reflected in the option premiums (puts increase and calls decrease).
OK, you have seen many of your ITM short calls assigned early before ex-dividend and you have never seen a short-put assigned early before ex-dividend. Therefore, your finite experience with these negates conversion, reversal and discount arbitrage?
Here's what I suggest. Provide an example of an ITM call that has time premium but where that time premium is less than a pending dividend and demonstrate that it is more profitable to exercise the call than to sell it. Provide the stock and strike price, premium and dividend.
ITM covered calls are exercised early because when there's a pending dividend, they often trade at a discount. If a call seller (STC) accepts less than parity, the buyer will immediately do a discount arbitrage, something the call seller could have done himself to avoid the haircut. This discount arb itself has nothing to do with the dividend.
Citing Alan Ellman of The Blue Collar Investor as a rebuttal isn't a winning argument. He has it wrong. He has carved out a nice niche in the covered call department but he falls short when it comes to a deep understanding of options.

