That's my experience anyways.
I do like a referral however. I often get cold emails from recruiters that are interested in hiring me, but still want me to fill out an application and do some intro async coding screen. It feels silly. I’d think I’d they’re reaching out, then why do I need to fill out an application? Let’s have a convo with the hiring manager, see if our goals align, and do the on-site grilling thing, if so.
By "let's do i anyway" do you mean to implement it? That's a terrible strat. You should not be touching the keyboard until you have an optimized or at least final design. If coding up the naive algorithm gives you some "insight" that you don't expect to have seen by thinking through the problem beforehand, you need to invest more in logical thinking.
This applies to both interviews and to your normal work.
In real life, it’s going to take you longer to understand the problem enough to even attempt the naïve solution. So in the context of an interview, get ANYTHING working.
Don't worry about the degree. After ten years (even after five) it doesn't matter. If it does matter to the company in question, you probably don't want to work there anyway. Seriously.
Lean heavily on your contacts. After ten years you almost certainly know good people at other companies, and you may be surprised how well they regard you. Most of my jobs have been through such connections, and they have been the ones I've enjoyed the most. Reach out.
During interviews, I find it helpful to communicate a little of my emotional state as well. "Let's see, I'm pretty nervous, just so you know, and I'll probably make a few mistakes here until I get it right. Now, the obvious thing is N-squared and clearly terrible, but let's do it anyway and see if we can get some insight and improve it..." And once you decide to have fun with a problem and can stop pretending that you're a giant, perfect brain, I've found things go a lot better. If your interviewer is an emotionless robot, you probably don't want to work with that person.
My own lack of a degree has never been a problem. You're fine, man. As long as you keep up some kind of continuing self-education (doesn't need to be fancy, just read interesting conference proceedings, maybe learn a new language every few years) you're going to do great.