Well, let me see if I can stir up the scientific need for one.
If anyone wants to see how counterintuitive – from an evolutionary perspective – the problem of the origin of protein fold superfamilies (FSF) can become, watch this talk, to the Royal Swedish Academy of Sciences, by Charles Kurland of Lund University in Sweden. I’ve timestamped the relevant starting point:
Kurland and his co-author Ajith Harish have been arguing vehemently in a series of publications for a FSF-rich LUCA – not a minimal cell, but rather one packed with “three fourths of the unique protein domain-superfamilies encoded by extant genomes.” (As an aside, Kurland can be amusingly blunt in this talk; e.g., “Rational thought is not a tool among phylogenists, actually” – ouch.) This inference of a domain-rich LUCA, of course, raises the question of the origin, or mode of origin, of the starting FSF abundance.
In a 2015 paper, Kurland and Harish are characteristically blunt. What they call the “seductive” model of continuous movement through protein sequence space, promoted by (for instance) John Maynard Smith, during the dominance of gradualistic or classical neo-Darwinism, won’t work. Cells do not tolerate the transitional states required to span the sequence and functional distances between discrete FSFs, but use sophisticated housecleaning machinery to sweep them out:
Nevertheless, a problem not solved by the modular assembly of natural proteins remains. This is the issue raised by Maynard Smith  when he asked, “Are all existing proteins parts of the same continuous network, and if so, have they all been reached from a single starting point?” The answer that might have been attractive to molecular biologists in 1970 was that indeed there might have been one or a few ancestral proteins. But, that answer is not now so obvious given the lack of homology between different SFs.
Of course, the epistatic editing system is made up of proteins and that system or pathway may not have evolved before the ancestral cohort of circa 1500 SFs belonging to MRUCA’s SF repertoire had evolved. In that eventuality, three fourths of all the extant SFs in modern genomes may have evolved under conditions in which SFs with sequence homology to other SF-coding sequences were tolerated. Presumably, this tolerance could be maintained until a minimum diversity of functions had evolved in the SF repertoire . After that minimum diversity of SFs was attained, the fitness of the ancestral cells might have been improved by the implementation of the epistatic editing system. That is to say, the epistatic editing system may not have laundered the proteins evolving during an earlier period of cellular life.
During this putative earlier epoch the rates of evolution of novel proteins may have been much more rapid than in modern times precisely because the editing of misfolded proteins was minimal. Of course the cost of such facile structural evolution is more frequent cellular accidents due to aggregation of misfolded protein.
(From here: The phylogenomics of protein structures: The backstory. - PubMed - NCBI)
Notice that Kurland and Harish have to suspend the normal cellular rules to derive the rich FSF diversity needed in the LUCA starting set: “The evolution of novel proteins may have been much more rapid than in modern times.” In terms of abductive logic, this parallels directly the move made by many workers who study the Cambrian Explosion: the pace of developmental evolution, modifying phenotypes, was dramatically different back then, to such a degree that we can no longer expect to observe such evolution today.