Personally, I have been running my computers this way for many years now. I do not use Linux kernel, but like "tinycore" everything fits in RAM. Size range is usually about 13-17MB for x86.
The USB stick or other boot media with the kernel+bootloader can be removed after boot. Depending on how much free RAM I have to spare, I can overlay larger userlands on top of this, and chroot into them. With todays RAM sizes, I can hold an entire "default base" (BSD) in memory if desired.
This filesystem on the media is not merely an "install" image. It has everything I need to do work, including custom applications. If I want distributions sets I download them; they are not stored on the media.
In normal use, I do not use any disk. Therefore I do not use a swap file.
Recently on HN a discussion of sorting came up, and I mentioned the issue of sorting large datasets using only RAM, no disk. Obviously BSD and other UNIX-like kernels date back to a time of severely constrained memory and are designed around space-saving concepts like "virtual memory" and "swap", "shared libraries", etc.
When one runs from RAM with no disk, working with large files means "thrashing" is a real possibility. Aside: Did the architects of virtual memory contemplate a world where users are doing work without using HDDs or other writeable permanent storage. (Start a new thread if want to answer/debate this.)
Sorting large files is something I do regularly so I am always open to new ideas. Currently I use k/kdb+ for large files instead of UNIX sort.
Here's the reply I got: