I don't think I have a great GitHub profile, and my personal website is still a joke https://DoctorDerek.com with no content, but I've had hiring managers tell me my projects are impressive. Here's what I always include in the README of my projects:
📛 Badges (Vercel, CodeCov, Build Status from Travis-Ci or another CI/CD service)
🃏 Project Title + Technologies Used (such as Next.js + React + Tailwind CSS + XState)
👀 View Production Build at ___
📃 Description
🎯 Feature List
📎 Discussion Section
🧠 Installation / Usage Instructions
⚙️Technical Journal
That's something easy for a hiring manager to skim that gives them a ton of context and clearly demonstrates that I didn't copy-paste the work from somewhere else.
Combine that with including numbers in my resume (reduced download size from 4500KB to 500KB; upgraded infrastructure for websites generating $10B in annual revenue), and it's pretty easy to stand out as a candidate.
You make a ton of great points that I totally agree with, like why we use private repos, why side projects don't get finished, why out-of-date portfolios are worse than useless, etc. I just use take home assignments from jobs to refresh & boost my portfolio, and that works great for me.