I believe we'll achieve ASI, but it will be both narrow and finite in capability.
We already have ASI in Go, Chess, some video games.
In those domains, infinite amounts of training data can be generated; and correctness of output is trivially and quickly validated. Imagine that: Absolutely perfect training data, available in unlimited quantities. This is the stuff of Singularity dreams.
Of course, these are also toy systems. Not like the real world. And even here, our superhuman systems aren't godlike. Give a human Go master 5 stones, and they will likely beat AlphaGoZero. SuperIntelligence, even narrow, isn't infinite.
Math as a domain is possibly as precise as Go, though orders of magnitude more complex and non-finite. If any important domain will show SuperIntelligence next, it's likely to be formal math. Even there, the gains will likely be incremental past those of humans, and comprehensible to humans, for the foreseeable future.
Coding, at first glance, shares many of the characteristics of these SuperIntelligence-plausible domains. Yet it is orders of magnitude more difficult to verify than even pure mathematics, and brings in the complexity of translating human language requirements to formal systems.
Most of human work and thought doesn't resemble these domains at all. The possibility space is infinite. Yet training data is finite or expensive. Verification is slow and subjective. Training data is mostly capped and also full of errors. SuperIntelligence may be possible in broader human domains, but we have no hard evidence that it is, and the hurdles are much higher.