One of the positive and negative purposes of a universal draft was to create a society where everyone learned about each other and to cooperate with each other. In the early days of the State people were coming from all corners of globe and there was a need to homogenize society quickly so it could work together. That's the positive side and I support that. The negative is that the homogeneous society that the government and army wanted to produce was a secular, leftist Ashkenazic one so the army was tasked with taking all those multicultural people and converting them.
The secular Left, especially the kibbutzniks, have always seen the army as their private property. They've always had resentment to how the Dati Leumi flocked to serve with enthusiasm and thought they too could have a say in how the army is run. So yes, this observation of yours is consistent. They sure want all the religious to enlist but they want them to cut off their peyos and start eating bacon on Shabbos by the time they're released. The idea that they'd stay in the army and also stay religious isn't something they favour.

Contrary to what the term means in America, to the Israeli left, "Messianics" means "anyone who believes in the coming of Mashiah". To that, I say that the army should include only "Messianics" and kick everyone else out.

Herzl himself was inspired by messianism. Check out the story of the messianic dream he had back when he was 12.

"Messianics" is a code word for "Religious Zionists," plain and simple. (Or, at best, "Religious Zionists I don't like.") Bear that in mind whenever you see the word. It doesn't include charedim and has nothing to do with actual beliefs. Lapid and Lieberman use it this way all the time.