Oh?
People, animals, birds and such all like getting off their heads, or modifying their perceptions and neural states. This means you have an inbuilt market for it all, one made from the very fabric of life. It is similarly not the sort of thing you might break the desire for by having it absent for a generation or two.
Being animals as well then many of the same chemicals work here.
Chemistry is such that you can turn useful everyday chemicals into other things. TiHKAL and PiHKAL are two books which cover this extensively. Also serves to show that we don't know everything to ban it -- the "legal highs" thing popular a few years back being a culmination of this.
Even if by some miracle that was stopped, everything was known, every combinatorial effect and digestion effect* was known for essentially all of the population** (you get things like certain people are immune to certain things -- painkillers are a fun one here, see history of laughing gas for an early one, and today certain people are noted as being immune to various other painkillers, by similar extension you also get people hyper sensitive to various chemicals) you still have the borders to contemplate. How do you propose to secure them from everything from seeds, yeasts and spores of plants and fungi to importers with obscene financial incentives to get around them (as it stands many of the cartels have money to burn here on all sorts of terrifying cool stuff, in that scenario... hard to even imagine how much)?
*there was an interesting patent case a while back. In it an unarguably new chemical was made but it was noted that upon ingestion it reverted to a known and patented chemical, thus was deemed patent infringement.
**at this point you have such an understanding of biology and medicine that it is probably tantamount to the biological equivalent of the unified theory of physics but we will assume it anyway. Would also yield some interesting things, and possibly some of the drug vaccines like we saw floated a few years back (
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2936703/ https://www.asam.org/resources/publ...le/2014/10/15/cocaine-vaccine-research-review ). To say nothing of people then being able to piss off abroad or something to get a nice drug producing implant.
Said chemicals do also have more than just "illicit" uses -- see some of the work done with MDMA and grief. As you presumably can't lock everybody up that is taking them with a massive layer of checks and balances on usages of substances then much like people sell their prescriptions now then what goes here?
To say elimination is possible very much overlooks the reality of things.