The Talmud (Sukkah 2b; cited also here) implies that chinukh (educating children in halacha observance) necessitates that the mitzvah be fulfilled according to its halachik details (at least with regard to shiurim [minimum/maximum physical dimensions]; see Ritva)
See also Shulchan Aruch Orach Chaim 657 and Biur Halacha there:
כדי לחנכו במצות - ופשוט דצריך שיהיו ד' מינין כשרין כמו בגדול
...in order to educate him in the commandments - and it is obvious that the four species must be valid as for an adult.
Nonetheless, there is a whole industry marketing chinukh-objects that do not conform to halachik requirements/shiurim, e.g. the popular children's tzitzit that are not the minimum requirement to require tzitzit, or invalid "chinuch" arba minim (4 species) sets (both of which further entail the potential prohibitions of brachot l'vatala [blessings in vain].)
Are there any authorities who allow teaching children mitzvot using objects that are halachically invalid for their performance? (Rav Ovadiah Yosef, z"l, permits chinukh with a borrowed lulav on the first day of Sukkot. However, he still requires that the lulav itself be kosher for the owner.) What bases are there to justify common practice? Does anyone discuss the permissibility of selling/keeping these items?