I would expect no less even in an introductory text. Mathematics is meant to be precise and formal mathematics even more so. Prosaic pedagogy might suit a liberal arts introduction but it won't help the reader to convince themselves that the statements and theorems proposed are true and valid.

The syntactic approach is really useful as a programmer. A Logical Approach to Discrete Math[0] teaches programmers how to develop proofs in this style using logic and syntactic substitution. Once shown how easy it is to achieve rigour it is hoped that work-a-day programmers can formulate their own proofs and develop stronger specifications using mathematical tools.

I'm not a formally trained mathematician and am completely self-taught as a programmer but with some background in set and graph theory I found it approachable. It's certainly a good companion text to learning more practical systems like TLA+ or Lean.

[0] https://www.amazon.ca/Logical-Approach-Discrete-Math/dp/0387...

Great that it works for you, but it won't convince anyone of anything if they don't understand what it means or why they should care.

As a writer or a teacher, if you want to reach a broad audience, give some simple, concrete examples, then explain the abstraction that covers them all. Assuming mathematical maturity won't help you reach your audience.