I see where you're coming from but I think it's more accurate to call them manipulative. Violence has a different connotation and we should keep them separate. Trying to force one thing into another is also manipulative.

If you truly believed that words can be violence, then logically you condone a physical response (eg hitting, shooting, etc.) to said verbal violence?

None of that changes word meanings. Violence is physical: https://en.wikipedia.org/wiki/Violence

If you asked most people, out of this context, if remembering an ad jingle or having one stuck if their head had a negative, positive, or neutral effect on them what would they say?

I don't have any studies, but this is the first time I've heard anyone state this as a negative. Most people don't seem bothered or might even associate a good time with some jingle.

What you just wrote is violence, since it caused me to feel defensive and anxious and also think about it more than I'd like.

You can easily draw lines between "I go to Hackernews.com to read the opinions of others and encountered an opinion I don't like" and "I have to listen to ESPN commercials at the gas pump and look at Jesus billboards when I'm driving down the highway". Other states have precedent for banning billboards actually.

If you want to take the other extreme of your extreme example here, you should be ok with people driving down the street and blaring advertisements from trucks at full volume day and night.

I'm sure upthread was being sarcastic.

The trend to conflate violence and words is dangerous. While words can lead to violence, to say that words are violence tacitly allows physical retaliation for speech that the listener does not like. We learnt as children this is wrong, and it remains so for adults.