For a finite abelian
$p$
-group
$A$
of rank
$d\,=\,\dim\,A/pA$
, let
${{\mathbb{M}}_{A}}\,:=\,\text{lo}{{\text{g}}_{p}}\,{{\left| A \right|}^{1/d}}$
be its (logarithmic) mean exponent. We study the behavior of the mean exponent of
$p$
-class groups in pro-
$p$
towers
$\text{L/K}$
of number fields. Via a combination of results from analytic and algebraic number theory, we construct infinite tamely ramified pro-
$p$
towers in which the mean exponent of
$p$
-class groups remains bounded. Several explicit examples are given with
$p\,=\,2$
. Turning to group theory, we introduce an invariant
$\underline{\mathbb{M}}\left( G \right)$
attached to a finitely generated pro-
$p$
group
$G$
; when
$G\,=\,\text{Gal}\left( \text{L/K} \right)$
, where
$L$
is the Hilbert
$p$
-class field tower of a number field
$K$
,
$\underline{\mathbb{M}}\left( G \right)$
measures the asymptotic behavior of the mean exponent of
$p$
-class groups inside
$\text{L/K}$
. We compare and contrast the behavior of this invariant in analytic versus non-analytic groups. We exploit the interplay of group-theoretical and number-theoretical perspectives on this invariant and explore some open questions that arise as a result, which may be of independent interest in group theory.