I don’t think it’s the certification standards, really. Yeah, they were a little outdated in some ways, but they weren’t the primary impediment to so much of GA. I don’t even think it’s the requirements for production under Part 21 (which, don’t get me wrong, are still a pain).
Rather, I think the biggest problem is the requirement that private, non-commercial owner-operators of light airplanes must maintain their aircraft in strict conformance to approved type design over the entire life of the aircraft. Nearest I can figure, that came in because either (a) the FAA figured they needed standards for commercial aircraft, just made one set of “one size fits all” standard, and then has refused to change things on the basis of “we only have one set of rules so there can only be one set of rules”, or (b) they figure that every airplane could theoretically be used commercially, and therefore all airplanes need to be conformed at all times just in case. Either way, it’s my belief that the vast majority of these owner-operators do not find this requirement to always be in strict conformance to approved type design to be a major benefit to them, and would be perfectly happy to convert their airplane to another category that frees them from that requirement–even if it’s a permanent one-way conversion (the FAA thinks otherwise, but I think the market would value such aircraft more).
The FAA itself (in the Par 23 ARC report that eventually led to the Part 23 update) even realized this and proposed that older GA airplanes be released from that requirement (look up “primary non-commercial”) and more or less be treated like homebuilts. Unfortunately, the rest of the FAA has been slow to follow suit. I’m holding out hope that this MOSAIC thing eventually leads us down this path.