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TL;DR
If you aren't doing software development, or working with a business or product-development model (or even just a company culture) that lends itself
poorly to small, cross-functional teams, then the https://agilemanifesto.org/ or the https://www.scrum.org/resources/scrum-guide may not be your best options. However, any large-scale system that doesn't have an intense focus on integration—and therefore a cross-functional skill set at least at the organizational level—is pretty much doomed to fail. Your mileage will not vary.
You present some anecdotal evidence about why your organization can't or won't do cross-functional teams or processes, and mostly point to the fact that cross-functional processes aren't necessarily cheaper, may not reduce overhead, and for various reasons make certain individuals or teams within your organization unhappy. Those things are often true but largely beside the point. Rather than argue those points, I will instead address why cross-functionality is pretty much de rigueur for any form of successful development and delivery (small or large), where it's mandated within Scrum, and some systems-thinking alternatives and further reading if you decide you want to take an alternate approach to implementing the required cross-functional integration processes to whatever it is you're actually trying to do within your organization.
Cross-Functionality and Integration Must Exist, Especially at Scale
In this section, I will address why cross-functionality always exists in successful systems, especially large ones. I will also address where Scrum mandates that teams be cross-functional, although you will need to do a lot of additional reading to understand some of the empirical control theory behind why it does so. I will also introduce the notion of systems thinking, which is essentially lacking from both your problem description and the solutions space you are grappling with.
Cross-Functionality is (Pragmatically) a Universal Requirement for Successful Delivery
Is cross-functionality a concept that bleeds in any sufficiently big software-architecture?
Cross-functionality is not mandated by all frameworks, but all projects must be fully cross-functional especially at scale. This can be done in-house by having all the needed skills on one or more teams, or can be done by outsourcing specific skills or pieces of program/product delivery outside the organization, but one way or another you have to have all the needed skills somewhere in your matrix or the project(s) fall apart.
Cross-Functionality is Mandated by the Scrum Framework
What is the book-recommendation for doing scrum without cross-functionality? Is CF mandatory to begin with?
If you plan to do Scrum, or a framework based on Scrum (e.g. SAFe or Nexus), then it is mandatory. Specifically, the very https://scrumguides.org/scrum-guide.html#scrum-team says:
Scrum Teams are cross-functional, meaning the members have all the skills necessary to create value each Sprint.
Furthermore, attempting to redefine "Scrum" without cross-functional teams make whatever you're doing Not Scrum℠. The Scrum Guide says:
The Scrum framework, as outlined herein, is immutable. While implementing only parts of Scrum is possible, the result is not Scrum. Scrum exists only in its entirety[.]
so while you're free to adapt the framework in any way you see fit, the end result cannot be Scrum if you aren't leveraging cross-functional teams.
Systems Thinking
Scrum may or may not be a good fit for your organization, product, or company culture. That's fine; there are other agile and non-agile frameworks to choose from. However, what you really seem to have is an X/Y problem where you're not taking a truly systemic approach to your organizational and systems-development structure.
One of my favorite authors about systems thinking and IT organizational structure is Bob Lewis. He's been writing about these sorts of topics since at least 1993, and if you https://issurvivor.com/?s=sub-optimize carefully you will find no less than 44 articles that discuss one of his most valuable phrases:
To optimize the whole, you often have to sub-optimize the parts.
This is core to lean and systems thinking. The goal is to optimize for the system (whatever you conceive that to be) rather than to optimize each team, department, or project. Cross-functional teams don't always optimize for organizational, budgetary, or HR concerns, and definitely don't optimize for the individual happiness of I-shaped people or the managers who hire them.
Suggested Reading
While there is a lot less hard science behind the Scrum framework per se, there is a lot of science backed by research and hard data behind systems thinking and the lean approach in general. If you want science and data rather than a more pragmatic approach such as Scrum (which leverages both empirically-proven and well-researched approaches without necessarily pretending to be either one in the academic sense), keep in mind that project management and systems optimization are continuously evolving fields, so any list is both subjective and potentially dated by the time you read it.
That said, you should definitely read books by Drucker, Deming, Poppendieck, Lewis, and anything to do with queuing theory (if you can handle the math) to understand why successful agile principles are generally based on small teams with predictable batch sizes that have frequent inspection and integration points. Especially in larger systems, the predictable cadence of inspect-and-adapt cycles and routine integration points are typically the biggest problems organizations have when operating at scale. Of course, that also means those cycles and integration points are arguably the most important locations to place your cross-functional people and processes within the system.