What kind of person bombs a city full of children, the elderly and other people who are not involved in the war? - Some even supported the stormcloaks before the war in Whiterun. Besides Whiterun, he wanted to repeat the same atrocity with Solitude.
Yes, the Empire also attacks Windhelm to try to capture Ulfric, but you do not see children running around in a bombing in the city, which is virtually isolated from civilians during the war. The Greybeards are quite clear the shout should never be used for personal gain, only in the worship and honour of the gods. Whilst Ulfric challenged the Solitude Jarl to combat (the Stormcloaks say it was a fair challenge by Nordic custom), he used the unfair advantage of the Shout against him, against the Greybeards' beliefs. Ulfric is Xenophobic and tolerates racist attitudes in Windhelm.