The homotopy fiber construction analogous to Arakelov motivic cohomology works for any orientable cohomology, and gives a long exact sequence involving suitable cycle class maps. For Weil cohomologies many of these cycle class maps might possibly be zero for weight reasons. Compare this with Jannsen’s “amazing to realize” remark, saying that some vanishing of some groups is equivalent to some deep conjectures. Can we apply devissage/descent arguments to such vanishing?
Jannsen (beginning of second page in Motives article): Parts of the standard conjectures would follow from the surjectivity of certain cycle maps, while the filtration conjecture would follow from the injectivity.
For p-adic regulators something can maybe be done? At least in the case of the talk of Mihailescu, Leopoldts conj is equiv to nonvanishing of the p-adic regulator.
nLab page on Other homotopy fiber sequences