User Stories are an Agile Practice, Independent of Kanban
"User stories" are an agile practice. They are not intrinsically part of Kanban. While many practitioners do use user stories as cards or work items in a Kanban system, this is not a requirement. User stories are common in Kanban because they are often easier and faster to estimate, not because the Kanban system requires them.
So, you can use technical tasks instead of user stories as your unit of work in Kanban. However, vertical slices and units of work that meet INVEST criteria such as small and indepedent are generally considered agile best practices, and you should follow those best practices unless you have a strong, overriding reason to deviate from them.
"The team can't/won't create vertical slices" is not a compelling reason. It often indicates a lack of agile buy-in from the team, a lack of experience in effective agile estimation, or a lack of training in agile practices and techniques. If the team gets measurably better results from doing something atypical, that's certainly a good reason to deviate from best practices. In the absence of meaningful metrics or a clearly-defined process problem that must be worked around instead of resolved, go ahead and do whatever works for your unique circumstances. Just don't make the mistake of confusing agility with lack of rigor; effective agility comes from establishing a predictable inspect-and-adapt cadence, rather than from Emotion-Driven or Personality-Driven Development™ practices.