Maybe I misunderstood your motivation for posting the question as you did, but I took your invocation of the term "architecture" to imply microarchitecture and not that of the instruction set as one generally refers to the Instruction Set Architecture as simply the ISA (reserving the "architecture" moniker for use as shorthand reference to the microarchitecture).
I can see now that if I substitute the acronym ISA for the word architecture in your post that your post does indeed capture the essence of the situation sans any and all conflationary concerns I had when I originally read it.
Okay, I could see why that would be confusing. I remember having that problem years ago. I'm used to people generally using "architecture" as shorthand for ISA and microarchitecture for a particular hardware implementation/family of implementations. I guess I took that convention for granted >_>
As for what others are saying re design capability..
I agree with the claims that Intel (and to a lesser extent AMD) have a substantial design advantage due to already having targeted high performance, and having less R&D money. But the question is just "can ARM make a high performance processor" (or maybe it's extended to "can someone make a high performance ARM processor"?), not if they can provide fierce competition with Intel, AMD, or IBM in single threaded performance. And until someone actually tries to allow a single ARM core to use a ~100W TDP envelope you can't say what the result will be.
You probably wouldn't see such an attempt in server markets because it's a losing battle to go for high single threaded perf at the expense of perf/W for high throughput wimpier core loads. ie, it's better to go for a niche and win some ground than go for mainstream where you can't compete at all. And you get better throughput perf/W results designing a CPU that can't clock past 2.5GHz than you do designing one that can clock past 4GHz. AMD is especially feeling this disadvantage.
Where we could theoretically see single threaded performance pushed higher for a custom design is in a console. Since they're on closed ecosystems the competitive pressure is different and the console companies still have an advantage in licensing or even owning processor IP, where ARM is potentially as good a choice as any. And power isn't constrained like in tablets and phones.
But I'm not really placing bets on that happening either.
Nonetheless, I wouldn't underestimate the ability of teams who have created decent low power designs to transition somewhat decently to high performance, just like Intel has transitioned somewhat decently to low power. Because a lot of big design advantages benefit both, and it's not like ARM cores today aren't employing several modern technologies, they're not just 1999 era processors. Although it's less obvious than it is with Intel's tick-tock progression ARM's designs have followed a reasonable evolution, with Cortex-A9 being a successor to ARM11 and Cortex-A15 a successor to Cortex-A8, and Cortex-A57 is clearly an improvement over Cortex-A57. No one's starting from scratch here.