Feasibility of bike frame design by a layperson I'm sure for many bike builders, their ultimate dream bike starts with a frame that they designed themselves. And herein lies the problem: it seems that modern means of frame production (e.g., hydroforming) implies very sophisticated shapes of frames, not just a bunch of round tubes welded together.

Is the design of a frame (together with rigidity calculations) something a layperson can reasonably pick up without taking a Mechanical Engineering degree? I'm curious about how all this stuff is actually learned and whether there are some places (training?) that explain it less than a few years.
Interesting question and way of looking at it.

Here's my take: those in the bike world who would seem most qualified to design scientifically optimal frames, which involves both mastery of all the advanced fabrication techniques and materials that are now available and the motivation to empirically figure out the handling and ride feel elements that can be hard to quantify, and which suffer when you just make things more stiff ad infinitum, usually end up working for companies where all the actual design decisions get made from a marketing and immediate profit perspective. The main question they spend their careers answering is, "How do we stay in the black in the next 2-3 years?" That's not to say that proper engineers aren't responsible for making some good bikes or moving the needle of progress and knowledge in the bike world forward, but they are not the only ones who do, and the mainstream companies they work for wind up pushing back the wrong direction on the needle quite often as well.

Small framebuilders usually aren't proper engineers, they usually don't have access to the same range of advanced materials and techniques, and they work in environments where myth, lore, and intuition can have louder voices than scientific process, but they're usually in a better position to deliver optimized ride feel and handling experiences to the end user. A lot of the major trends and advancements in the industry get started by non-engineers working at a grassroots level. And, to answer your question, you can get started in that world by riding, reading, geeking out, taking framebuilding classes (usually 1-2 weeks), and participating in existing forums.

Some other important pieces:

Round tubes start to have some meaningful disadvantages for high level athletes in high level competition. For everyone else all the rest of the time, bikes based on round and simple ovalized tubes aren't stiffness- or weight-impaired in any meaningful way.

If one does want to mess with more physically dialed frames, you don't have to be an engineer. You can just start doing carbon layups in your garage. Yes, without training you probably won't be able to do it with the same level of sophistication an engineer could. But you also won't be hamstrung by a marketing department or the need to make a product that has mass market appeal or that works for pros. So whether you actually wind up with a product that's any worse than theirs is not foretold by your lack of a degree.