I agree with the general concept of extending I-22 to 20/59 somewhere in the eastern part of the city, but IMO the best way they could build that would be to directly connect it at the 20/59 split. In theory, you keep the northbound truck traffic away from the middle of the city by forcing them onto I-22, and help Malfunction Junction as well.
However, that means it would likely go right through not only the airport, but a large cemetery as well. I don't know if it's feasible to go under the airport, either building-wise, or if the government would allow such a thing for security reasons. The alternative is to go around the southern end of the airport and build parallel to 20/59 until the split, then curve it over.
The 20/59 split is already tough to negotiate with the tough curves, but I presume it would be rebuilt anew as part of the construction. There's also the issue of the I-20 portion being only 4 lanes there with the long elevated section, and the intersection with US11 almost right on top of the interchange.
Beyond the airport though, it's a mainly industrial/railroad/open area so the "western" part of that connection should be easy to complete through Fultondale/North Birmingham, other than the topography of it.
You could also connect I-22 to 20/59 a little farther west around the Tallapoosa St. exit, but traffic backs up there as it is, so I can't imagine taking I-22 almost all the way through downtown just to avoid a 4 mile stretch to Malfunction Junction. Either way, IMO by building a connection that close to downtown, you're adding more traffic to the area immediately east of Malfunction Junction, which is the whole reason for the bypass. That little 3 mile area between Tallapoosa and the Split would make for all the difference in the world.