Tefillin on Rosh Chodesh

Why do we take off our Tefillin before Mussaf on Rosh Chodesh? Wouldn’t it be better to keep the Tefilln on for the entire davening in the morning? Isn’t the act of taking off the Tefillin disruptive to the Tefilla and the Kavana and individual may have? In the old days, when people wore Tefillin all day long, did they also take off their Tefillin for Rosh Chodesh Mussaf?

The Shulchan Aruch OC 423, 4; writes, that it is the custom to remove the Tefilin before Mussaf. The Mishnah Brurah explains the reason, since it is in a way a Yom Tov and on the Yom Tov we don't put on our Tefilin, likewise at least during the Mussaf when we mention the Offerings of the Rosh Chodesh we remove the Tefilin. The Tefilin should be removed in a way it does not interrupt the Kavanah of Tfilah.