In chapter 5.3 of the book Functional Analysis by Peter D. Lax, the author says
It is a fact of life that some Banach spaces are very rich in isometries; others are very poor. (...) Among the poor ones are the function spaces with the max norm. Here is an example due to Schur:
He immediatly tells us to consider the space of sequences of complex numbers that converge to $0$ with the max norm $||(x_n)|| = max |x_n|$. Then he tells us that for any sequence $(b_n)$ of complex numbers of absolute value $1$ that the operator given by $(Ux)_n = b_n x_n$ is an isometry. And that an operator given by a permutation of the terms of the sequences is an isometry. He finally says that compositions of these kinds of operators are the only ones.
This is a continuum-sized set of isometries. Why then does the author say that this space is very poor in isometries?
The gold standard for a "rich" collection of isometries is $\ell^2$. One way of quantifying precisely what is meant by "rich" here is, for example, that the isometry group of $\ell^2$ acts transitively on its unit sphere. On the other hand this is very far from true of the isometry group of $\ell^{\infty}$ which has many more orbits acting on its unit sphere.
When it comes to spaces this large just considering the cardinality is not a good way to measure how "rich" the isometry group is.