Tump was trying to build wall to prevent immigration. Drugs do not come from immigrants but from cartels through different means. Trump's idea has never been about stopping all commercial exchange at the border nor dismantling every single vehicle crossing the border in search of pills.
Additionnally, if cartels can't smuggle drugs through the border, they'll build fentanyl shops inside the USA.
Sorry, but you really need to listen to what Trump actually said instead of listening to his stuff filtered by the media. He definitely did say that the wall would help stop drugs. Even DEA law-enforcement agreed with him that it would help. And yes, there is a significant amount of drug trafficking carried out by people crossing the border. Whether they are "true" migrants or "cartel employed" is irrelevant.
"..they'll build fentanyl shops inside the USA..."
US law-enforcement would love this to happen. Damn easy to get a court order and bust up. Damn easy to setup informants to reveal such locations. Its like comparing peanut impacts versus asteriod impacts. You solve the critical asteroid problem first. The peanuts don't really make any significant difference.
"Unauthorized" border crossing (and otherwise innocent) immigrants are a key piece of the cartel smuggling apparatus. They are used as bait to overwhelm CBP resources (and asylum seekers often want to be caught, theyll be given a court date to make their asylum case and in many cases released), once the resources are overloaded the drug smugglers go through the rugged terrain to drop-off points.
That's what I would do, yes. Although I didn't mean to imply that with my previous statement. The closed border approach would be to somehow erect a barrier that lessens the ability for them to consume CBP resources between ports of entry.
Additionnally, if cartels can't smuggle drugs through the border, they'll build fentanyl shops inside the USA.