To be clear, if it he happened on and off that eliminates a bunch of potential causes. It is entirely possible this is just a loose ribbon cable or similar, though it could be a different kind of intermittent. Does it happen on an external monitor? What about a live USB? Both of those will isolate whether it is hardware or software to some degree.
What I have always wanted from a phone since Android came out is what I had with my HTC Dream (the first android phone, slide out keyboard, trackball, oh god, I loved it). I had a super chunky extended battery which made it last multiple days on a single charge, or for someone such as myself made it last the full day. My current phone has a 5003mAh battery and is 8.9mm thick. I would happily take something that was 20mm thick to have all that space taken by a battery, which based on the dimensions of the battery is about 0.17Wh/mm^3. The remaining space should provide enough space for about 23500mAh which would bring the total to just under 29000mAh. At my current usage of charging twice a day from about 20% up to 100%, so around 4000mAh x2, and assuming we want to work between 20% and 80% for extended battery longevity, that would make about 17000mAh or just over 4 days of usage. That would be a delightfully chonky phone with the easy ability to keep the charge within the healthy range, not to mention the ability to have it stand on its side or upright without a stand in many cases.