Packages are to be compiled and distributed as a unit. When considering what classes belong in a package, one of the key criteria is its dependencies. What other packages (including third-party libraries) does this class depend on. A well-organized system will cluster classes with similar dependencies in a package. This limits the impact of a change in one library, since only a few well-defined packages will depend on it.
It sounds like your logical, vertical system might tend to "smear" dependencies across most packages. That is, if every feature is packaged as a vertical slice, every package will depend on every third party library that you use. Any change to a library is likely to ripple through your whole system.
