Why is Jake even there?

Alonzo knew that the cash was buried under the floor so it was just a matter of arranging a way to get the "pusher" out of the way and steal his money. Having Jake along as a "virgin shooter" makes them look clean, which is just the way he planned it. He told Jake he planned it all week so he clearly had plans to use this clean, lilly-white, white boy as the shooter. He had him smoke some pot/crack which set him up where he had to go along.

Yes, the movie has some obvious plot holes(what movie doesn't when you watch it enough?) but it's pretty close to reality and definitely gritty as Hell....

^ I agree with Pope Duke.

The fact that Alonzo made this Jake's training day is also in line with Alonzo's character. He doesn't play it safe because he feels invincibly powerful. He feels he can manipulate situations as they occur & people as he reads their inclinations, so he would not be worried about Jake messing anything up.

Alonzo also plays psychological games with people much more than simply using brute force or thoroughly planning situations. He's less of a strategist than a manipulator; he gave Jake drugs to manipulate him, not to actually use it to invalidate Jake's story later (he would never let Jake talk to begin with; as shown when he left him to be killed later). He was using these situations as a test - will Jake join his crooked team or not? Can Jake be manipulated or not?
The movie title is a bit tongue-in-cheek, IMO - he is trying to train Jake to be a crooked cop.

Throughout the movie, Alonzo puts Jake in positions where Jake has to compromise his ethics a bit. Alonzo puts a spin on it to be sure, but he lets Jake know he can "get dirty" so as to catch big criminals or go to some desk job (as if those are the only two options; but he's asserting his own power at the same time). Jake does compromise a few times, but it's because he doesn't fully see Alonzo's crookedness yet (he's trying to believe it's justified). Involving Jake in these crooked incidents (for lack of a better word) is, as mentioned above, a golden opportunity to test Jake's character & see if he can be corrupted & manipulated.

A big theme in the movie is the idea that pure goodness does conquer evil. Alonzo keeps telling Jake you have to be a bit bad to conquer the bad. However, the only reason Jake lives is because of the good he did; the Mexicans let him go because he saved the guy's cousin (or was it his niece?). This may seem like a convenient coincidence in the plot, but it's a part of the theme. Even the people on the streets, as hardened as they are, ultimately respect Jake's moral strength over Alonzo's crooked power. This is Alonzo's blind spot, and why he'd be overconfident in bringing Jake along to begin with.

However, Alonzo begins to slowly realize that Jake's hesitance to go along with his crookedness is not cowardice but strength. In the scene where Jake puts the gun to his head, it fully registers to Alonzo that Jake is just as powerful as him, but in a different way. This is why Alonzo feeds him to the Mexicans to be killed. He knows Jake will not be corrupted, but also that he is NOT weak enough to be manipulated or scared silent, and so he knows that Jake poses a great threat to him. As I noted above, this was not a part of any strategy; Alonzo is confident to manipulate situations as they arise, in the event things don't go as he'd like (ie. Jake won't be corrupted).

That's sort of a tangent, but I think it explains why Alonzo would choose to involve Jake. Sure, there may have been some strategy involved as far as the plans for the day, but I think he mainly chose to involve Jake to break him in psychologically.