Partaking of the sacrament is a witness to God that the remembrance of His Son will extend beyond the short time of that sacred ordinance.
To further stress the sacred nature of this ordinance:
The ordinance of the sacrament makes the sacrament meeting the most sacred and important meeting in the Church.
Given how sacred the ordinance is, it seems given that children shouldn't be permitted to "play" Sacrament. For example, constructing their own version of the sacrament from bread and water in the kitchen and then serving to themselves.
However, understanding that young children often imitate things they encounter (these are young children we are talking about here, ages 2, 4, and 5), and that they clearly are not intending any disrespect or irreverence, it could also be looked at as a form of reverence in itself that they want to administer and partake of it as part of their play. Also, it is something they look forward to each week and there is concern that putting the kibosh on it during playtime at home may suck the fun and excitement out of it. Children can be particularly susceptible to shaming and guilting, and that does not seem appropriate. However it does seem important to teach them to respect the ordinance.
Is there anything in LDS teaching that addresses this issue, or is it a matter left entirely to the judgment of parents?