In Iwasawa theory, even if one is only interested in questions about a number field $K$ (e.g. class groups of $\mathbf{Q}(\mu_p)$, Selmer groups of abelian varieties over $\mathbf{Q}$), to prove deep theorems it seems that you often need to study arithmetic objects over $\mathbf{Z}_p$-extensions of $K$ to get results over $K$.

Are there conceptual explanations why this is the case?

For example, the $p$-adic $L$-functions live in the Iwasawa algebra, which depends on a $\mathbf{Z}_p$-extension, and the Euler systems I know are also defined over $\mathbf{Z}_p$-extensions, but is there a more high-level and better explanation?

The post of David Loeffler at Applications of Iwasawa Theory mentions http://staff.ustc.edu.cn/~yiouyang/colmez.pdf, but is there a short explanation?

In Iwasawa theory, even if one is only interested in questions about a number field $K$ (e.g. class groups of $\mathbf{Q}(\mu_p)$, Selmer groups of abelian varieties over $\mathbf{Q}$), to prove deep theorems it seems that you often need to study arithmetic objects over $\mathbf{Z}_p$-extensions of $K$ to get results over $K$.

Are there conceptual explanations why this is the case?

For example, the $p$-adic $L$-functions live in the Iwasawa algebra, which depends on a $\mathbf{Z}_p$-extension, and the Euler systems I know are also defined over extensions, but is there a more high-level and better explanation?

The post of David Loeffler at Applications of Iwasawa Theory mentions http://staff.ustc.edu.cn/~yiouyang/colmez.pdf, but is there a short explanation?