This practice began more than 40 years ago as one of the consequences of a deeper understanding of the communion rite. In the TLM low Mass (its most common form) the people didnt pray the Lord's Prayer aloud and didn't make any connection with "give us this day our daily bread" and the reception of Holy Communion. In those days the reception of HC was infrequent. Praying the Mass in a language people could comprehend led to a new understanding of receiving communion as not just a private act of piety but also as an expression of being united with Christ in all the members of his Body. Joining hands at the Lord's Prayer became one aspect of visibly expressing the faith of a community which prays "Our" Father rather than "My" Father. I don't remember any priest telling me that I should or must offer to hold hands with those nearby. Nor have I told anyone that as a priest. As the bishops stated there is no rubric directing people what to do with their hands during the Lord's Prayer.