O(1) in many cases involves a hashing function which is a non-trivial but constant cost. For smaller values of N it can be outperformed in terms of wall clock time by n^2 worst case algorithms.
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Besides, often you're lucky and there's a trivial perfect hash like modulo.
I also don't understand your first point. We can run n^2 algorithms on massive inputs given its just a polynomial. Are you thinking of 2^n perhaps?
Rockstar infamously wasted five minutes loading GTAV because they had an n^2 algorithm in the startup sequence.
In practice, n^2 sees surprising slowdowns way before that, in the 10k-100k range you could be spending minutes of processing time (10ms for an element would only need ~77 elements to take 1 minute).
It's a perfect hash function for the case where you work with ints and know the maximal min-max range beforehand; then you can modulo by the size of the range as long as it's not too large. In your example 33-21 --> mod 12
This comes up for me surprisingly often but obviously depends a lot on what you work on. It is often tempting to reach for a hashtable, but it's a lot less efficient in this case.