Other way round: the only way any company other than Intel was able to get a new instruction set launched into the PC space was because Intel face-planted so hard with Itanium, and AMD64 was the architecture developers actually wanted to use - just make the registers wider and have more of them, and make it slightly more orthogonal.
In that different world, Transmeta would actually succeed in the market of x86-compatible CPUs and, perhaps, would even come up with their own 64-bit extension. Itanium would still flop.
Or maybe, if the push came to shove, the desktops would switch to something entirely different like Alpha. Or ARM! Such event would likely force ARM to come up with their AArch64 several years sooner than it actually happened.
With how long it took Intel to ship expensive, incompatible, so-so performance ia64 chips - your theory needs an alternate universe where Intel has no competitors, ever, to take advantage of the obvious market opportunity.
It's true that most of those would have lacked the resources to replicate AMD's feat with AMD64. OTOH, AMD itself had to buy out NexGen to produce their K6. Without AMD and/or AMD64, there'd be plenty of larger players who might decide to fill the void.
The first generation was complete garbage. Itanium 2 came too late and it did not get widespread due to wrong business decisions and marketing. By the time it could have been successful, AMD64 was out. And even then Intel targeted only the same high-end enterprise market segment, when they have implemented 64-bit on Xeon: https://www.cnet.com/tech/tech-industry/intel-expanding-64-b...
We can't know for sure, but my guess is that Itanium still could have failed. I could imagine an alternative universe where, even with HP-UX and WinXP running on it, no one wanted to deal with porting their application software. And its emulation of 32-bit code (both in hardware and in software) was atrocious, so running existing, unported code wouldn't really take off either.
Eventually Intel gives up after motherboard/desktop/laptop makers can't build a proper market for it. Maybe Intel then decides to go back and do something similar to what AMD did with x86_64. Maybe Intel just gives up on 64-bit and tries to convince people it's not necessary, but then starts losing market share to other companies with viable 64-bit ISAs, like IMB's POWER64 or Sun's SPARC64 or whatever.
Obviously we can't know, but I think my scenario is at least as likely as yours.
In an alternative universe without AMD64, Intel would have kept pushing Itanium while sorting out its issues, HP-UX was on it, and Windows XP as well.