First, what sounds natural in English is of no relevance to what sounds natural in Japanese as the two languages are completely unrelated.
This "advertisement" is a creation of Japan Tabacco Inc., which is a private company; therefore, it is not a public announcement (at least by the Japanese standards). Since it is advertisement, it can have more freedom in its style of expression than real public announcements by a local or the national government, which would often tend to sound stiff.
Trust me, using the past tense is NOT a common practice in catch copies in Japan, either.
By saying 「たばこを持つ手は、子供の顔の高さだった。」, it makes us Japanese-speakers feel like we are readng prose --- a line from a novel or something. It kind of sticks in my mind, which is a good sign of success with mottos, catch copies, etc.
On its website http://www.jti.co.jp/tobacco-world/torikumi/manners/index.html , Japan Tabacco Inc. states, regarding this phrase (at bottom left of page) :
My freehand TL: "Instead of an ad like 'Let's stop ~~~!', we made an ad by selecting an ordinary scene that smokers would feel an intimate connection with and that would have them reflect on their manners and really "think"."