Just to be clear, I'm not arguing for lighting bolt to do physical damage.
I'm just not convinced of this clearness you speak of.
I found the part about elemental attacks in the drain table. About the only place I didn't look

. Although I'd say it is stated that way to make sure a clever spellcrafter doesn't try to get elemental spells with stun damage & mana spells drain modifiers, I agree now, elemental spells have to be both physical spells and do physical damage.
However I see no evidence that this is only there to allow for easier template use. It's quite possible that the intention rather was to make sure every elemental spell also does physical damage (which leads to said rules contradiction).
The same goes for your definition of "spell description". If the damage-type section was only referring to the part not written in the spell code why not just write "the damage can be found under spell effects". Moreover I have yet to find any evidence that the spell code is not part of its description. In german a description is defined as "a summary of information/details about something", which is exactly what spell code + effect do. Leaving one of them out just makes the spells description less complete.
I doubt that this is the intention and doubt the english definition of description is any different from the german one.
This of course leads to the "spell description vs. electricity damage" contradiction debate, which is just not so easily solved.
Even the part about the lightning bolt spell in the electricity damage just states "similar".
Similar ≠ the same.
In short, while from a logical point of view I'd agree with your argumentation, as it makes sense to keep exceptions to the rule down to a minimum, I still have to say your interpretation of the rules is just not as clear as you'd like it to be - especially as you argue "by the rules" in terms of wording and such.
As I've already written the closest you could come to "overruling" the physical damage from the spell code is by saying that even physical electricity damage is treated as stun damage. Then again a lightning bolt is only "similar" not the same... .
P.S. I don't want to sound nitpicking here, in fact I'm all for clearness, but rules wise it just ain't clear.
Also, I don't think real life examples do this discussion any good.. While I personally think that every pen & paper group should at the very least be inspired by how things work "in real life", the rather abstract rules set of shadowrun tends to crack when confronted with certain real life examples.
Take "Electricity damage" for example.
In real life leaves electricity burns due to the heat set free when it hits a human body which would fall into the "physical damage" category.
But Shadowrun doesn't take notice of that.
So when you go on, the whole set of rules gets questioned and crumbles.
Therefore it's much better to just stick to the rules, they work quite well in most situations and when they don't just pick the option your group likes best, or change whatever you don't like. After the rules are just a means to experience stories in playing your character in the shadowrun universe.