Not just Linear Algebra but every branch of Science/Mathematics should be taught as much as possible using Geometry (and other visualizations) before being mapped to abstract algebraic symbols. Basic Geometry (along with simple Arithmetic) is the oldest subfield of Mathematics for the reason that most of its concepts are intuitive and feels "natural" and mappable to the "Real World" by us Humans. While abstraction via symbol manipulation is necessary to generalize and extend mathematics it should come at a later stage after we have developed some intuition of the concepts being represented by the symbols, however limited/restricted they might be. All abstraction requires some mathematical maturity which can only happen over time.