It is necessary to be clear about the relationship between creativity and genius - and the relationship between genius and breakthroughs.
The following are some of my definitions and assumptions:
1. Genius is creative - it is a mixture of creativity and high ability (mostly intelligence).
2. Creativity is an aspect of personality - creativity is indeed part of the cluster of personality traits discovered by HJ Eysenck and called Psychoticism. The Psychoticism trait-cluster also tends to include various 'antisocial' or socially disvalued personality traits such as lower than average conscientiousness, lower than average empathy/ agreeableness, impulsiveness, arrogance etc. - these are, in fact, necessary components of creativity.
3. Because intelligence and personality are mostly hereditary, so are the components of genius - but the necessary particular combination is rare.
4. Because intelligence and personality averages and distributions are different between human groups, so is the incidence of genius - some societies have a much higher percentage of geniuses than others; but this incidence is never very high, and may be zero.
5. Because genius has been defined in terms of psychological attributes, the assumption is that these attributes will tend to lead to the achievements which are associated with genius - but not necessarily. A person may be a genius, but for various reasons (bad luck, inhospitable society, underdeveloped culture, illness, persecution etc) fail to make a major achievement.
5. On the other hand, I assume that ALL major achievement (all major breakthroughs) are made by a genius - whether correctly attributed to a specific genius person, or not. Apparent counter examples, e.g. when major breakthroughs are apparently made by people of high intelligence but low creativity (or to 'teams'), will (I believe) almost-always be found to depend on the work of an unattributed creative genius (or pair, or very small number) - and if that person cannot be identified, I assume that they nonetheless existed.
6. Therefore, without major geniuses, there are no major breakthroughs.
But genius is relative - in the sense that creative people of lower ability, and less luck, may make important breakthroughs at a smaller societal scale, and perform as 'local geniuses' uniquely able to solve local problems (whether credited for doing so, or not).
I have (provisionally) termed these 'local geniuses' Patagonian Shakespeares.