Pole at infinity and zero at finite frequency
a pole at an infinite frequency ...

No.

RC Low pass filter has a finite pole and zero at infinity and it
makes sense

Low pass will be
\$  H(s) = \frac{1}{1+s}\$ and it has no zero. It is not the same as &quot;zero at infinity&quot; , which is not really a thing, and would be
\$  G(s) = \frac{s-\infty}{1+s}\$ and for any \$s \in \mathbb{C}\$ it would be ill defined.