Adam Clarke on Deuteronomy 16:21

Thou shalt not plant thee a grove, etc. - We have already seen that groves were planted about idol temples for the purpose of the obscene worship performed in them. (See on Deu 12:3 (note)). On this account God would have no groves or thickets about his altar, that there might be no room for suspicion that any thing contrary to the strictest purity was transacted there. Every part of the Divine worship was publicly performed, for the purpose of general edification.