Why reusing e2e tests output is bad?

I understand that the consensus is that each test should be independent in order to avoid side effects affecting other tests, but consider the following scenario.

I have n features f_1, ..., f_n. Each of them requires other features (a subset of them) to be executed in order to test the ith f_i. For each feature there is an end to end test t_i, which executes the corresponding feature and its dependencies and then makes some assertions on the feature under test.

Argument: the all set of test executions is a boolean expression t_1 AND ... AND t_n. So, for each t_i, we can describe it as f_i AND f_j AND ... for each dependency f_j of feature f_i, because if a dependency fails, the all test fails (it can't arrive to evaluating its assertions).

So the whole test execution could be represented as a BDD (https://en.wikipedia.org/wiki/Binary_decision_diagram) and reduced. Basically when I make a test, i reuse the output of a previous test which encompasses all the dependencies of the feature under test, for which assertions have already passed. Of course this means tests should have a precise scheduling order.

What's wrong with my idea? Thanks for the dedicated time.