In 'Sicario', what was the purpose of raiding the tunnel?

In Sicario, the job of Matt's (Josh Brolin) task force is to:

1. Disrupt operations for US-based drug boss Manuel Díaz, so that he'll get called back to Mexico to answer to his boss, Fausto Alarcón.
2. Track Díaz when he goes there, so they can learn Alarcón's location.
3. Have Alejandro (Benicio del Toro) kill Alarcón.

To achieve this, they track and freeze Díaz's bank accounts in the US, and Díaz does indeed get called back to meet with Alarcón. They track him perfectly with aerial surveillance as he drives there. End of story, right?

Yet throughout the movie, they've also been trying to find Díaz's drug tunnel under the US/Mexico border. They find it around the same time Díaz is called back.

While Díaz is driving to Mexico, the task force raids the tunnel. As planned, the task force draws fire, which lets Alejandro slip through the tunnel to Mexico. There, he forces a Mexican police officer (and drug mule) to intercept Díaz's car on the highway. Alejandro hijacks Díaz's car, has him drive to Alarcón's house, and Alejandro does his deed.

My question is: Why was the tunnel ever important?

They've already disrupted Díaz's operations, and he's already on his way to meet Alarcón, so it's not that. They're not really interested in arresting drug mules or confiscating anything. I doubt they're even interested in shutting down the tunnel; they've got their eyes on a much bigger target. They just kill everyone in the tunnel and high-five each other. And for some reason it's very important that this happens at the same time Díaz is driving to meet his boss.

Yes, they use the tunnel to get Alejandro into Mexico, but this seems like a crazy way of doing that. Heck, they just drove to Mexico earlier in the film. Sure, that was in five big trucks with some US Marshals and Special Forces and a Mexican police escort, but I'm sure they could also manage something a lot more subtle. I don't think the CIA would have too much trouble getting a Mexican guy into Mexico.

And yes, using the tunnel allows Alejandro to hijack the police officer's vehicle, as the guy is right by the exit of the tunnel. But that's happenstance. The officer is just a random drug mule making a delivery. Could've been anybody.

Of course it's fortunate that he's in a police cruiser, since Alejandro uses it to get Díaz to pull over, but that just seems like improvisation on Alejandro's part. It even involves the police officer actually acting like a police officer making a traffic stop, not a drug mule meeting his boss. Not that the mule knows who Díaz is, or Díaz knows him; they're on vastly different levels in the hierarchy. So it's not like this particular officer is "their ticket in" or something. His association with the cartel doesn't enter into it at all.

It just seems like it'd be a lot simpler to track Díaz's car all the way to Alarcón's location. They've got drones and cameras trained on it all the way it seems. So why not just have Alejandro on stand-by in Mexico? Once they know where Alarcón is, he can strike. By car-jacking Díaz, they risk him fighting back, getting away, alerting someone, or simply driving Alejandro somewhere else entirely.

It's one thing for Díaz to play right into their hands (even driving during the night when the tunnel raid, the hijacking, and infiltrating Alarcón's compound are all more feasible). But then it seems they just turn around and jeopardize the whole operation.