I'm posting this hoping it will help someone else. I'm not a MD or in any related field but I had the same problem and it took me almost 2 years to figure it out. I ride and train 15-20 hours per week and lift 2-3 days per week with an RPE of 8 or 9. I normally ride 6-7 days per week, following a polarized training plan with a mix of hard interval session, long endurance days, and some active recovery sessions as needed. In January, I put 108 hours on the bike and felt completely fine, maybe just a little fatigued. However, when I finally do take a rest day, there's probably around a 50% chance that when I get back on the bike, I can't even turn the pedals without extreme pain in my quads. If I take 2 days off, there's closer to a 75% chance this will happen, and 3 or more days, its 100% chance. The pain can happen in either leg and in any of the 4 muscles in either quad. I tried diet changes, supplements including calcium, daily stretching and core work, but nothing seemed to help. One more important detail to mention, I am software developer so I spend long hours at my desk daily (this is actually what got me into cycling to begin with).
As the season is about to start, my training was going great and my numbers were looking better than ever, then I found myself back in the cycle of pain and off the bike after spending a few days in the hospital for the birth of my son. As the days started to pass, I was resting but it seemed like my condition was getting worse, not better. After more and more searching, I finally found an article from the Cleveland Clinic that was my "ah ha" moment. Many cyclists and runners have IT band problems but that didn't seem like it was my problem because the more I rode the better I felt. However, this article also mentions that many people also experience IT band issues from sitting at a desk with your knees bent for hours at a time. After reading that, I thought about it, and every time I take a rest day, its a work day, so therefore I sit all day, eat dinner, then wind down with the family and go to bed. After 3 days of a cycle like this, its no wonder I couldn't get back on the bike for a workout. I remember Pogi's coach saying that on rest days you want to do as little as possible, but I was even doing that wrong. To test my theory, I decided to spend an entire day off the bike but on my feet doing stuff around the house. The following day, I went for a ride and my legs still had some soreness but the pain was gone. As of this writing, I think I'm back on track and my season isn't going to wasted after all. I really hope this helps someone else. Here's a link to the Cleveland Clinic article some possible things you can do to help:
https://health.clevelandclinic.org/it-band-stretches-and-treatments-to-relieve-knee-and-hip-pain