"I went from Tokyo to Osaka on the Shinkansen."
Unless you are reading something that is meant for little kids (like Pokemon), a majority of Japanese words are written in Kanji. If they are not common use Kanji, they will have their reading displayed alongside them, called ふりがな。
I've seen しんかんせん used a lot more often than the kana for city names. I don't know if this is for marketing or for tourists with beginner Japanese. Another consideration is that public transport is also used by young children so many signs are in hiragana for them since they can't read kanji yet.