That's the way socks were first knit. Before the invention of dpns or circular needles, knitters had to knit socks on straight needles. I wanted to try this for myself and I found a very easy pattern for doing so. Best thing of all, it was free!
The Easiest Knitted Socks Ever
And it is easy. The author gives the pattern that fits their foot, so you'll have to adjust for your own foot. Any competent knitter can do this easily. However, I did make a couple of other changes.
I made short row heels and toes rather than decreasing/increasing at heel and toe. When they're sewn up they look like short row toes and heels. I also didn't go down as many stitches as she did. I have wide feet and heels, so I only decreased 16 stitches at the toes and heels. I also didn't need as many rows for the bottom of the foot. Only 30 rows. I also added a couple more rows of top ribbing (for 6 rows), which made the top ribbing an even inch in width. As I made changes, I noted them down in notepad in a condensed format since this sock is a plain, stockinette sock.
Here's a couple of in-progress photos of it, so you can see, I'm using straight needles and knitting both socks at the same time. Though I'm only knitting them *almost* flat. Doing it like this and I'll only have to close up the two side seams, since the heels and toes are already done.
Now, to go this route, you will have to do each heel and each toe separately. I didn't cut my main color when I did the toes and heels since I knew I could just pick it back up for the last purl row of the short rows. All in all, it's been a great knit. I'll post finished pictures when I finish them. I'm already almost finished with the insteps, so I'll just need to knit the front of the leg and the ribbing. I'm toying with a stretchy bind off for that since this sock is basically a top-down/toe up sock. We'll see.