Here's my take. If Kries was the one responsible for the DP moves, he deserves to be fired. Villa was good, he's the brightspot DP move. Brining on old Frank Lampard when you already had Diskerud was the first mistake. The second was by City's ownership who then kept Lampard in Manchester so he could ride the bench. If you wanted Mix, don't get Lampard, if you wanted Lampard don't get Mix. Those 2 moves together didn't make sense. Instead they could have gotten ALtidore as a striking partner for Villa or Kljestan as a more versatile midfielder (which is how they're using Mix but Mix isn't that type of player) gotten a winger in Farfan or a promising young central mid in Pelosi. Anyway just a waste. Imagine if you would they were the ones to go all out and get Villa and Giovinco instead of Villa and Lampard? ANy number of scenarios IMO work out to be better for NYCFC than getting Lampard. After that the real ****up happens and that's going full stupid and bringing in Pirlo. Pirlo is extremely talented, BUT he plays Serie A as a position who's job it basically is to be a passer and that's it. That doesn't exist in MLS because the league is so athletic driven. Without the talented players at the end of his passes who know the system Pirlo is basically worthless. Could be the worst DP signing since Rafa Marquez.
Rumor was that Kreis didn't really want Pirlo at all, and was ambivalent about bringing in Lampard midseason, but upper management overruled him and he tried to make it work. I don't know how true those rumors are, but given Kreis' personality they seem to fit the mold. Remember, Kreis doesn't hold the keys to the roster like a European coach, that goes to GM Claudio-Reyna.
To be clear, I think you can make Villa, Lampard and Mix work, make Lampard a CAM and have Mix play on the right, as he has done successfully for the USMNT before, played with a true CDM, that could work extremely well. Alternatively play a 4-5-1 with two CAMs in Mix and Lampard, again with a true CDM and wingers.
Adding Pirlo into the mix is an issue. Pirlo in Juventus typically played in a 3-5-2 or 4-3-3, surrounded by defensive players so he could focus on putting service into the forwards; in that sort of setup speed isn't as much of an issue and Pirlo didn't have to defend. NYCFC isn't set up like that though, they're in a 4-4-2 formation that relies on the midfield clogging things up, and Pirlo doesn't or can't do that. With Pirlo you have two players (Lampard and Pirlo) in the midfield that don't defend, Mix is something of a two-way midfielder but he's not a dedicated defender. That leaves you with one midfielder that's truly defensive, and for NYCFC that man is Andrew Jacobson. To be clear, Andrew Jacobson isn't bad as far as CDMs go, but he's no Ozzie Alonso or Dax McCarthy, the sort of player that can absolutely shut down attacks with great positioning and sheer grit, he's a journeyman with a lot of experience in MLS.
To be quite blunt, NYCFC's problem is not Jason Kreis in my opinion. The mothership expected playoffs in the first year, and that's just not realistic for an expansion team. Ownership thinks that if you throw enough money at it, you can become great in MLS almost instantly, and that's simply not the case.