I suppose the real question is, why close the Schwab Platinum when you can close your Vanilla Platinum? The answer here largely depends upon what you use your points for. It is a somewhat lazy approach to the rewards game, but I just dump all of my points into my Schwab brokerage account at a rate of 1.1 cpp (RIP 1.25 cpp) and invest from there. The hope there is that tossing a few hundred bucks a month into ETFs will ultimately (literally) pay off dividends. I know that I could very likely find better redemption rates for travel/hotel stays (and then invest the money saved on the flight/hotel) but I do not enjoy the hunt for these deals and ultimately I don't want the best redemption dictating my travel plans. If you invest your points or even if you hope to cash them out, then keeping the Schwab open over the Vanilla makes sense. One counterpoint, and someone correct me if I am wrong, but I believe the Vanilla Platinum sometimes receives offers/promotions that the co-branded cards do not.

As halamadrid pointed out, one popular line up is the Amex Platinum / Amex Gold / Amex BBP (often referred to as the "trifecta"). This trio of cards earns you 5X MR on Hotel/Air, 4X MR on Restaurants/Groceries, and 2X MR on Miscellaneous categories. Put against the 1.1 ccp redemption rate with Schwab, that's 5.5%, 4.4%, and 2.2% cash back on those categories.

As you've noted the Delta Platinum is a decent sock drawer card because the Companion Cert and Delta perks more than cover the cost of the AF provided that they're used.