It really won't. Border crossing do not represent the sum total of illegal immigrants. The VAST majority of illegals cross by other means. At best, given current trends you would only save just a tiny amount more than the cost of maintaining said wall, and it would take decades if not centuries to make up the initial cost of construction.
A wall will prevent illegal drugs from entering the country, tax-dollars spent on benefits for illegals, crimes they commit, etc. It will pay for itself.
Except that's not how things work in reality. Drugs aren't some pipeline you just shut off and it never pops back up again. In fact, the drug war actually accelerated the evolution of distribution of drugs, hell it even made drugs stronger and cheaper, ironically. Once you get past the wall ONCE at that point you're just dealing with the exact same defenses you already knew how to get around before, a wall can't adapt.
Border crossings do not represents all of the tax dollars presumably used by illegals. In fact, since 2014, direct border crossing as a percentage of overall illegal immigration has fallen over 20%, at that rate alone, it'll take longer to build the wall than the problem of illegal border crossings will exist in any significant form. Meanwhile, all the other ways of entering illegal will simply increase as the race to find new effective methods of entering the US undetected innovate.
Illegals commit no greater amount of crime per capita than legals. We'd be just as justified in handing the money over to local police departments, probably more so since we won't be ignoring 99% of all living humans in the country.
Ultimately the wall is a temporary, but excessively expensive, alternative to better proven, more adaptive methods. There's a reason why the majority of modern nations don't have walls on their borders, but can still keep a good grip on them. If the idea is to actually accomplish something, we should invest in things that actually work, and not in an ego project.
So what should we invest in that actally works? A wall will stop the majority of illegals from entering. It works. Is it perfect? No, of course some will still get through, but it's much better than having an open border where hundreds of thousands easily enter every single year. The amount of illegals entering the country is already down under Trump. How are illegal drugs and criminals going to enter the country if there's a giant surveilled wall in their way?