Let's talk about that failed drive then with more specifics, because most of those running plays were creative and worked well. We had to punt because that 6th running play failed on a 3rd and 1 but even that call looked decent.
For starters, it's impossible to analyze defensive alignments in real-time from the broadcast footage. What Geno sees is not what you see as the viewer, and any real analysis depends on the endzone angle which the NFL hasn't been releasing until Wednesdays this year. Takes before then can only be guesswork, no matter how many likes the person posting about it has.
1st and 10 - 3 yard rush
Hawks come out in 12 personnel while the Saints are in big nickel with CGJ lining up on the strong side in wide 9. The Saints have DTs at 2i and 3 with DEs at 5 strongside and 9 weakside (LEO). That leaves the strongside B gap and weakside A gap "open", but they have a Mike and a Will at the second level with the LCB cheating up with eyes on the strongside B gap.
Geno sends Everett on a jet sweep towards the strong side of the formation while handing the ball off to Collins who is heading for the weakside A gap.
The offensive line is angle blocking to the weak side and have a blocker for every defender. Brown and Lewis clear out the RDE and RDT respectively and Fuller does an OK job getting to the Will LB. Gabe Jackson gets bulled into the A gap by Ringo, which forces Collins to hesitate and then Ringo makes the tackle. While it looks like Jackson is primarily the one who gets beat, it's very possible that Fuller was supposed to briefly double team Ringo before moving to the second level. That's something that they do a lot, including on the unsuccessful 3rd and 1 later in the drive. Either way, it looks like Collins probably should have had at least 5-6 yards if the OL had blocked Ringo better.
2nd and 7 - 6 yard rush
The Hawks swap to 11 personnel and the Saints respond with a bizarre pass rush package pulling their DTs off the field. They have their Mike LB lined up inside as a 1 tech (threatening blitz), three wide DEs and then two safeties at the second level. I have no idea what the Saints were thinking here but it looks like Geno calls the correct strongside run play for a decent gain. One of the wide aligned DEs is just a second late to Collins in the backfield, so maybe it could have worked but they shelved that alignment after one failure.
3rd and 1 - QB sneak for 1st down pickup.
I won't dwell on this one. The QB sneak always looks good when it works and bad when it doesn't.
1st and 10 - 4 yard run
The Hawks go back to 12 personnel with both TEs now lined up on the left side of the formation (making it the strong side). The Saints respond by mirroring their first alignment, except their Mike is now way over to the strong side to cover the Dissly if he runs a route. The Hawks angle block down to the weak-side and have three blockers for three defenders. Unfortunately it looks like Shell and Jackson miscommunicate as both pick up the LDE which allows the Will LB to get in front of Collins and force him to cut back. I'm tempted to put this one slightly on Jackson as he looks a bit lost at the snap but we'll never know. This one had more potential then it was blocked for.
2nd and 6 - 5 yard run
Hawks are in 11 personnel and the Saints are again light in the box with six defenders (4 DL 2 LBs 2nd level). This looks like Geno is checking to the run but that isn't clear from either the broadcast or endzone footage.
The strong side of the formation is to the right as Dissly lines up next to Shell, and the line angle blocks to the strong side at the snap. Collins does a very nice job on this play being patient, reading the hole, and then hitting it and keeping his feet going to work himself up field.
3rd and 1 - 0 yard run
This is the one rush that doesn't work, and it ends the drive as a result. It's again unclear whether this play was changed or not; the Saints defense is trying to line themselves up until the snap but that isn't dispositive. The Hawks are back in our heavier 12 personnel package and the Saints bring out something new, with their DTs two gapping inside, DEs supporting the B gaps, and two safeties threatening a blitz.
It looks like our offensive line wasn't well coordinated here. Cameron Jordan throws in a last minute wrinkle by shifting inside immediately before the snap, but the right side of our line gets clogged up and Fuller kind of ends up blocking nobody. In hindsight, this may have been worth spending a timeout or possibly this is one of the reasons why we saw Pocic get back onto the field as soon as he was healthy enough to play.
If we are looking specifically to blame the coaching staff for this punt then I would focus on the execution of the last play and the blocking assignments. I don't see a problem with any of the six play calls. They make sense in context, they aren't running into disadvantaged situations (usually the opposite), and all six are completely different concepts (as is the defense each time).