Boeing / Airbus Market Share
There's a lot of too and fro in the debate about which company is doing best. However, I think the data in Wikipedia is fairly conclusive. This Table shows the aircraft actually in service across the worlds airlines. It shows that in the 14 years from 2006 to 2020, the in-service share shifted from Boeing:Airbus 2:1 to nearly 1:1. That's a huge swing in market share from Boeing to Airbus, in quite a short time (aircraft last in service a lot longer than 14 years). That's reinforced by the fact that, today, Airbus has thousands more aircraft on backlog than Boeing. Even more tellingly, what with the MAX grounding and COVID, Boeing has taken quite lengthy "delivery holidays", whilst Airbus continued to deliver at quite a high rate even during the COVID pandemic.
One of the reasons why long haul airline tickets are so expensive at the moment is because Boeing has massively under-delivered. Consequently, leased aircraft are at a premium on the rental market as aircraft that have expired their hours are grounded and have not been replaced. You can tell how badly this is affecting the market when airlines are dragging A340s out of storage and putting them back into service. Even the A380 now looks like good sense (Even Qantas have restored their entire fleet to operations).
Continued contraction for Boeing seems guaranteed, especially given that the CEO / board has said they're not really going to do anything about this by investing in new designs. The problem with this is that, with Boeing's performance continuing to be eratic, collapse seems highly likley, and probably sudden.
To Airbus, market share has been their key driver. You can make money if you have market share. You can't make money if you don't have market share. What Boeing has found is that, whilst their inefficiencies could be hidden and ignored when they had high market share, they can no longer be ignored now that Airbus has pinched a big slice of the market. A real indication of this is that Airbus, despite the commercial failure of the A380 program (as big an inefficiency as you can get) none the less managed to survive and thrive. How bad can Boeing be that they couldn't make Airbus really, really hurt with the failure of the A380?
Too Big to Fail? US Gov Military Motivation to Support Boeing?
I think you overestimate the extent to which the US gov is prepared to support Boeing. The US Military have had issues with a lot of Boeing made products of late - Apache, KC46, P8, Airforce One.
Apache - a mature, legacy programme - was inexcusable; the US Army sent a whole batch of brand new ones back because of poor quality manufacturing.
KC46 has had innumerable issues such as poor quality, it not being usable as a tanker at night, and its cargo floor clamps spontaneously letting go of cargo containers. It was and is a nightmare procurement for the USAF. Boeing used every dirty trick in the book to beat up the USAF to win the contract, and then delivered a shite aircraft.
P8 has recently stopped production because of a supplier issue.
Airforce One is very late. And, the cost of saving Boeing to the sake of future AF1's is probably more than the cost of a future bespoke design. For example, Airbus spent about $25billion creating the A380; it's going to take more than that to save Boeing. Paying Lockheed or Northtrop to do a one-off design is probably cheaper.
In short, there's not many reasons at the moment for the US Military to love Boeing.
Meanwhile, Airbus has at least one reason to be loved by the US Military, who clearly want the A330 based MRTT tanker (which is what everyone else in NATO is buying). Airbus, properly teamed up with a US prime like Lockheed or Northrop, could find its successful commercial designs being picked up by a number of US military programs.
Domestic Politics and Geopolitics
An actual Boeing collapse would be a huge issue, because all of a sudden it'll not be legally possible to fly a large fraction of the world's aircraft fleet. Certified flight operations depend on manufacturer-backed "design authority" support, which will have disappeared. That's the part that's "too big to fail".
Plus, if Boeing collapsed with thousands of aircraft still on the order books, it's not like Airbus could fill the gap quickly. That starts getting geopolitical, very quickly. The US Gov and Europe would not want a Boeing-sized hole in the commercial aircraft market filled by a Chinese State backed manufacturer. Some very strange things might happen, e.g. the US Gov asks Airbus to come in and pick up the remains of Boeing, keep plants operating, etc.
The ideal for the democratic West is that Boeing is restored to industrial, engineering and economic health. Aviation is important to the global economy, and no one in the West wants China to gain control of that aspect of it. It's therefore worthwhile pondering, how has Boeing got into this mess in the first place, to know how to fix it? It's related to how US businesses behave and are incentivised, how employment in the US works, and so forth. Boeing has chased profits and cost reduction because that's what shareholder have obliged them to do, and in doing so has accumulated vast debt, lost a ton of market share, has a poor product line up, and huge labour issues (e.g. they've just lost hundred of experienced engineers who've had to retire, due to the contract between the company and the union). You cannot permanently fix this simply by pouring money into the company. It takes wholesale reform of how business operates in the USA. That's a deeply political issue, and one that the US political system is uniquely ill equipped to address.
What's going on round the world is that everyone is looking at the USA / Boeing, to see if the US is actually going to do anything about it. They seem not to be doing anything (apart from a belated attention to certification practises). Some airlines are evidently buying Boeing partly because they're worried if they don't, Boeing CA will collapse and then there won't be any choice.
Airbus too are rumoured to be worried about a Boeing collapse; becoming a global monopoly would attract the most dreadful political heat. It's known that, in launching the A320neo family, Airbus were taking a bet that this would bump Boeing into (yet again) revamping 737. When Boeing responded with the MAX, apparently there was champagne popped open in Toulouse, because Airbus knew they could out-profit another 737 derivative. Then the MAX crashes happened.
I don't know for sure, but I strongly suspect that Airbus seniors are now a little bit worried that they might just have overdone the whole "attack Boeing's market share" thing, sowing the seeds for big problems for Airbus in the future. There is competition, and then there's deadly competition. Airbus now know that if they corner Boeing even more, there's a danger that the consequences can be fatal. It's pretty bad way to do business knowing that if you're too good at doing it, your (incompetent) competitor might end up killing people again trying to keep up. At least the FAA seems to have sharpened its regulatory teeth again, to keep things minimally safe.
One way out of this is to allow Airbus to continue to become truly vast at a high pace, to get to a point where (from everyone else's point of view) Boeing is small enough to fail, ASAP.
Another way out is for the US Gov and European Governments to realise that an alliance on commercial aviation is needed. If a global monopoly is going to be the eventual result, why not arrange that in advance and avoid the chaos? That could involve the US admitting that, "Okay Airbus, you win", but ensuring a smooth transition from Boeing making (defunct) Boeing designs to the same people in the same facilities coming under Airbus-style mangement building Airbus designs, and the whole Airbus vs Boeing thing being buried for good.
There is already precedent for this: this is exactly how Airbus got formed in the first place - an amalgamation of European aircraft manufacturers. A politically backed merger between Airbus and Boeing is no different in concept.