For Linux this may not be an issue for long. Linux on ARM is gaining some traction in the Cloud with AWS and it's also on Chrome Books and other low end edge devices. MacOS on ARM may even nudge things along.
I don't think Linux is going to be a problem unless you're a developer who needs to build and test x86 binaries. The whole ecosystem is founded on source-level compatibility and hardware independence, most of the major open-source packages are already up and running on ARM64 and the major distros have pretty complete ARM versions of their distributions. The only uncertainty is whether anybody will be able to produce a (stable, usable) "bare metal" distribution with compatible installers, bootloaders, drivers etc. for the Apple Silicon platform where almost
everything is done by proprietary hardware in the ASi SoC. However, Apple have
shown Linux running under virtualisation - which is more convenient than dual booting for many applications - so that much is a done deal.
VMware has experience in virtualization. They haven't demonstrated any experience in emulation and given that there's little demand for enterprise level emulation of this style, it seems unlikely that VMware would be interested.
There's a lot in common between a desktop hypervisor like VMWare Fusion or Parallels and a "software emulation" beyond the actual engine that actually makes the guest binary code run. VMWare or Parallels would have a huge head start on anybody else - and they're both big enough and ugly enough to buy in experts or license technology to bolt an x86 emulator/translator on to their virtualisation products.
If you look at the open source solution,
QEMU, it already "does it all" - virtualization, full-system emulation and "user-mode emulation" (which looks vaguely like a 'Rosetta for Linux'). Since there is already a QEMU port for iOS (albeit non-App-store-friendly and with a laundry-list of restrictions) and people have also had it running on Raspberry Pi, that will quite likely turn up for ASi Macs in due course, if nothing else does.
NB: There's already a "Hypervisor kit" framework built into x86 MacOS that does the basics of virtualization - Docker for Mac uses it, as does (I think) the App-store-friendly version of Parallels (There's certainly an option to use it in full Parallels) and it would be the smallest surprise of the year if Parallels for ASi at WWDC was using it. Conceivably, Apple could also add an "emulation kit" using Rosetta technology if they felt that x86 emulation was a must-have.
Back in the day, Connectix Virtual PC emulated a x86-CPU on the old PowerPC Macs (also two completely different architectures). With nowadays processors being much more powerful, I don't know why a solution similar to that would not work unless I'm missing something.
Yes, that would absolutely work and may well appear (if nothing else, someone will likely get the open-source, cross-platform QUEMU running on ASi in the fullness of time).
Trouble is, the performance of such emulations has always sucked and - although processors have got faster (and emulation/translation software has improved) - software has got more demanding. It deals with one class of problem - e.g. running that one bit of non-demanding admin-ish software that you sometimes need for work or letting you program that lump of industrial machinery - but probably won't be up to running graphics/video/audio/number-crunching software the way bootcamp or hardware virtualisation could.
The ability to run Windows natively on Intel Macs can't be underestimated.
There's no question that some people will have to switch to PC (or at least get a second machine) because of the ASi switch - but I suspect that it is far less of a big deal to many than it was in 2006. Computing has changed, and for a lot of people those 1-2 bits of Windows software they couldn't live without are now websites or mobile Apps ("most" of which will now run native on MacOS - although I'm waiting to see what "most" turns out to mean).
A big part of Apple's laptop customer base will be delighted if their new ultra-thin MacBook can play 4k video in a browser tab for 50% longer on a single charge. Some will be happy if their 16" MBP can run FCPX without thermal issues. Others want an iMac they can use for music production without the fans blasting - or a Mac Mini that isn't knobbled by the only lowest-common-denominator iGPU that Intel offers on desktop chips.
Presumably, Apple have done their market research and decided that those people outnumber (or outspend) those who need
high performance x86 Windows.
It's highly likely that there will eventually be
some way of running x86 Windows under emulation and/or virtualizing ARM Windows. Also, now that more people have broadband and faster WiFi, there's the possibility of using Remote Desktop to access a PC in the cloud, at work or tucked away under the desk. (Even with Linux you can spin up an x86 server in the cloud for $5/month). The users who need performance will always be a niche squeezed between what you can do with virtualisation/emulation and the far better bangs-per-buck you can get if you just buy a PC.
Personally, running Windows and Linux has been hugely useful to me in the past but, with the growth of mobile and web technology, creating a Windows binary that users have to install is a last resort if a web app will do the job, and
the demise of Internet Explorer (and the failure of "legacy" Edge) in favour of Chromium greatly reduces the need for firing up Windows for testing (...last time, that meant I wasted ages chasing what turned out to be a Parallels bug, and I'm eventually going to need a Surface Pro or something
anyway to test things on touchscreen).
OTOH, the current Intel Mac lineup really doesn't float my boat and I'm liable to switch to PC anyway if Apple doesn't offer something new - which is what Apple Silicon promises.