Exponential functions do not have singularities. There would have to be some additional property of the curve in order to conclude the presence of a singularity.
I agree that "the Singularity" is not a singularity in the mathematical sense of divergence, but it is a singularity in the sense of a singular (i.e. special or unique) event. (If it happens at all, that is.)
Look twenty years out and it appears vertical. But 10 years from now it will look much flatter, and what's then 20 years out (30 years from today) will look vertical.
The grass is always greener 20 years in the future.
As I understand it, "the Singularity" refers to the point in time where AGI becomes better at improving itself than the humans that created it. Then the existing exponential growth gets replaced by another exponential, but with stronger feedback.
It's the difference between a differential equation like x' = x and x' = 10x . In either case you can say "meh, if you normalize on today's value, the increase in 10 years is just a constant multiple", but the transition from one phase to the other will still be noticable, even though things won't "go vertical".