As with most things I think the success of ARM has less to do with its chips or architecture and more to do with its business model and the competition.
For decades the combined power of Intel's volume and Window's ubiquity kept a huge amount of resources dedicated to that platform. SPARC, M68K, NS32, VAX, PA-RISC, even Itanium were crushed under the unrelenting focus by third parties on building tools, software, and systems around x86 and later AMD64 architecture chips.
What is fascinating is that Intel got into that position by being open, there were no fewer than 12 licensees for its 8086 design, and people had supplanted "expensive, proprietary lock-in" type architectures with more open and cheaper chips. It was the emergence of the PC market, and the great Chip Recession of 1984, where Intel decided if it was going to stay a chip maker, it had to be the best source of its dominant computer chips. I was at Intel at the time and it shifted from partnering, to competing, with the same people who had licensed its chips, with the intent of "reclaiming" the market for CPU chips for itself.
You have to realize that at the time the bottom had fallen out of the market, and things like EPROMs and DRAM (both of which Intel made) were being sold on the grey market at below market costs as stocks from bankrupt computer companies made it into the wild. Further competitors like Ok Semiconductor were making better versions of the same chips (lower power, faster clock rates). Intel still had a manufacturing advantage but it could not survive if it couldn't make the margins on its chips hold. It dumped all of its unproductive lines, wrapped patents and licenses around all of its core chips, and then embarked on a long term strategy to kill anyone who wouldn't buy their chips from Intel at the prices that Intel demanded.
We can see they were remarkably successful at that, and a series of CEOs have presided over a manufacturing powerhouse that was funded by an unassailable capture of not only software developers but system OEMs as well. They fended off a number of anti-trust lawsuits, and delicately wove their way between former partners like Compaq who were now laying on the ground, mortally wounded.
ARM was playing in the embedded space, dominated by the 8051 (an Intel chip) where Intel played the licensing card (just like ARM) licensing its architecture to others who would make their own versions of the chips. As a licensing play they insured their partners would never move "up market" into the desktop space and threaten the cash cow that was x86.
The relentless pace of putting more transistors into less space drove an interesting problem for ARM. When you get a process shrink you can do one of two things, you can cut your costs (more die per wafer), or you can keep your costs about the same and increase features (more transistors per die). And the truth is you always did a bit of both. But the challenge with chips is their macro scale parts (the pin pads for example) really couldn't shrink. So you became "pad limited". The ratio of the area dedicated to the pads (which you connected external wires too) and the transistors could not drop below the point where most of your wafer was "pad". If it did so then you're costs flipped and your expensive manufacturing process was producing wafers of mostly pads so not utilizing its capabilities. At the Microprocessor Forum in 2001 the keynote suggested that spending anything more than 10% of your silicon budget on pads was too much. 90+% of your die had to be functional logic or the shrink just didn't make sense.
The effect of that was that chips ARM designed really had to do more stuff or they were not going to be cost effective on any silicon process with small feature sizes. And the simplest choice is to add more "big processor" features or additional peripherals.
So we had an explosion of "system on chip" products with all sorts of peripherals that continues to this day. And the process feature size keeps getting smaller, and the stuff added keeps growing. The ARM core was so small it could accommodate more peripherals on the same die, that made it cost effective and that made it a good choice for phones which needed long battery life but low cost. The age of phones put everything except the radios on chips (radios being like modems, different for every country, were not cost effective to add to the chip until software defined radio (SDR) became a thing. And the success as a phone platform pushed the need for tools, and the need for tools got more of the computer ecosystem focussed on building things for the ARM instruction set.
At that point step two became inevitable. Phones got better and better and more computer like, they need more and more of the things that "desktop" type computers need. You have a supplier (ARM) which is not trying to protect an entrenched business basically doing all it can to widen its markets. And a company like Apple, who wasn't trying to protect its desktop/laptop market share pushing the architecture as far as it can. More tools, more focus, more investment from others to support it, and like a fire that starts as a glowing ember near a convenient source of tinder, the blaze grows until the effects of the fire are creating its own wind and allowing it to grow bigger and stronger. Even after Intel woke up to the fact that the forest around their x86 architecture was on fire, I don't think they had enough time to put it out.
So here we are with ARM chips which are comparable in software support and feature set of Intel's low end desktop CPUs. But without the Intel "tax" which is the extra margin Intel could demand being the only player, and immune to Intel's ability to attack by patents or license shenanigans. Intel is in full on defense, paying tablet vendors like Lenovo to use their chips in ARM tablets, supporting the cost of building out their own IoT infrastructure with Galileo, and doing all they can to keep ARM out of their castle, the data center. Like DEC and its VAX line, or Sun and its SPARC line, they are doomed.
Looking at the performance of the iPad pro it is pretty clear you can build a chromebook or a laptop that would meet the needs of the mass market with an ARM architecture machine. And because ARM licensees can add features anywhere in the architecture including places like the frontside bus[1] which is tightly controlled space in x86 land, you will be able to provide features faster than x86 OEMs can convince Intel they need them. And that will change things in a pretty profound (and I think positive) way. Not the least of which might be having the opportunity to buy a lap top that isn't pre-backdoored by the chip manufacturer with its SMM.
[1] Literally if you buy a bus analyzer (a sophisticated logic analyzer) from Agilent or Tektronix and hook it to the Intel frontside bus, it won't display the signals until you enter the NDA # you got from Intel! That is pretty tightly controlled.