But generally speaking, ARM pushes for going wide, and X86 pushes for more IPC on fewer cores (pipelining, out of order execution, etc).

Going wide also means having more superscalar units and therefore getting better IPC. You also don't really understand what pipelining does. Using pipeling increases IPC versus not pipe-lining sure, but adding more stages actually can reduce IPC as with the Pentium 4. This is because it increases the penalty for misprediction and branching. Excessive pipeline stages in a time before modern branch predictors is what made the pentium 4 suck. The reason to add more stages is to increase clockspeed (pentium 4) or to bring in more complicated instructions. The way you talk about this stuff tells me you don't actually understand what's going on or why.

Also x86 has had memory controllers on CPUs for well over a decade now. Likewise PCIe, USB, and various other things have also been moved to the CPU - north-bridges don't even exist anymore. Some even integrate the southbridge too to make an SoC much like a smartphone. None of this is actually relevant to the architecture though, they are entirely down to form factor, engineering decisions, and changes in technology which are relevant to the specific chip or product. If x86 had succeeded more in smartphones and ARM had taken the desktop (as was there original intention) then you would be stood here talking about x86 chips including more functions and ARM chips having separate chipsets. So this isn't a fair thing to use to compare x86 and ARM.

It's also not really true that x86 has fewer cores. A modern Ryzen in even a laptop form factor can have up to 16. That's more than Apple put in their mobile chips. I get why people think this way. It's because phones had 8 cores long before PCs, and because it made sense at the time. When ARM cores were smaller and narrower and had much less per-core performance and IPC increasing their number made sense. Likewise more smaller cores is more energy efficient than fewer bigger cores, and this makes sense for something like a smartphone. However nowadays when big, wide, power hungry ARM cores exist and are used in higher power form factors than a smartphone there isn't really the need to have so many. At the same time x86 have efficient small cores these days that in some cases get better performance per watt than their ARM equivalents, and x86 core count has skyrocketed. Both of these platforms were originally focused on per core performance too, as multi-core consumer devices simply weren't a thing. All of this "ARM has more cores and x86 has more single core performance" malarkey was only true for a certain window of time. It wasn't where this all started and it's not where we are going now. Instead what we are seeing is convergent design where ARM and X86 are being used in the same use cases, using the same design concepts, and maybe eventually one will replace the other. Only time will tell.