Is "liturgical dancing" permitted at Mass? I've seen it once or twice, and it looks silly and irreverent to me, like some kind of pseudo-interpretive ballet in which one person gets up and slowly dances while everyone else just sits and stares, feeling uncomfortable.
You have put your finger on one of the key reasons why liturgical dance is not permitted during liturgies in the West.
In 1975, the Vatican's Congregation for the Sacraments and Divine Worship issued Dance in the Liturgy, which it declared is to be treated as "an authoritative point of reference for every discussion on the matter."
The document noted that although there are cultures in which dance retains a religious character and could be permitted in liturgy,
the same criterion and judgment cannot be applied in the western culture. Here dancing is tied with love, with diversion, with profaneness, with unbridling of the senses. . . . For that reason it cannot be introduced into liturgical celebrations of any kind whatever: That would be to inject into the liturgy one of the most desacralized and desacralizing elements, and so it would be equivalent to creating an atmosphere of profaneness which would easily recall to those present and to the participants in the celebration worldly places and situations.
The document went on to note concerning the pseudo-ballet you mention, "Neither can acceptance be had of the proposal to introduce into the liturgy the so-called artistic ballet because there would be presentation here also of a spectacle at which [only] one would assist, while in the liturgy one of the norms from which one cannot prescind is that of participation [by all]."
This remains the law today. In 1994 the same Vatican congregation ruled:
Among some peoples, singing is instinctively accompanied by hand-clapping, rhythmic swaying, and dance movements on the part of the participants. Such forms of external expression can have a place in the liturgical actions of these peoples on condition that they are always the expression of true communal prayer of adoration, praise, offering and supplication, and not simply a performance. (Instruction on Inculturation and the Roman Liturgy, 42; italics added)