There are better presentations of geometry than the Elements :) (Plus, the original constructions, without algebra, are rather tricky and don't generalize well!)

If we're interested in the mathematical method and its power, a good start might be to, well, go with more exploration-based approaches, where students have to learn things in order to solve a "real"(-ish) problem. Of course, the training required and attention to students would rocket and is likely infeasible, but hey, if Euclid's elements in the original Greek are on the table, this doesn't look too bad !