This is how the routes looked in 1948:
The construction of the Dearborn Street Subway changed things somewhat -- the Logan Square line was routed into the subway, which then terminated at Congress Street rather than continuing on to the west -- but the Garfield (aka Congress) and Douglas branches continued to be run off the loop.
When construction began on the Congress Expressway, though, things changed considerably because the route of the new expressway interfered with the existing elevated structure. A long span of the Garfield branch -- from California to Racine -- was temporarily rebuilt at ground level to allow construction. The connection between the Lake and Logan Square lines proved its usefulness even after Logan Square was routed into the subway, when the Douglas branch, apparently no longer accessible from what was left of the Garfield elevated, was rerouted to take Lake Street to the Loop. (That track still exists as the connection between the Blue Line and the rest of the El system, though it is not in day-to-day use). The result was the following:
(with the usual Lake Street trains, not highlighted in this drawing, sharing the Lake Street El between the Loop and Marshfield). I don't know whether the Douglas and Garfield trains were through-routed around the loop or whether they operated independently.
When the Congress line was finally completed, Garfield and Douglas trains were taken off the loop and the Logan Square trains were routed through to the Douglas branch, now branching off Congress, and the Congress branch itself, basically as it exists today. If the 1948 CTA map is to be believed, though, the CTA originally had much different plans for the west side elevateds. Here is the relevant passage:
By 1950, the Milwaukee Avenue-Dearborn Street-Congress Subway is to be completed and in operation with new subway-elevated cars purchased by the CTA. This is the second of two lines financed jointly by the City of Chicago and the U.S. Public Works Administration. This second subway will serve an estimated 50,000,000 riders annually. Their individual time saving will range from 15 to 25 minutes per day.On the City of Chicago's construction program is a West Side Subway as an extension of the Congress Street leg of the Milwaukee-Dearborn-Congress Subway. Crossing under the Chicago river in tubes, it is to emerge near Halsted Street in the strip between the roadways of the Congress Street Superhighway. It is to continue in the median strip of the highway to Kedzie Avenue and then turn north in subway tubes to connect with the Lake Street "L".
Included in the plan are the construction of two track connections to the Douglas Park and Garfield Park branches at Marshfield Avenue and at Sacramento Boulevard, respectively.
If I'm interpreting everything correctly, the west side elevated system would then have looked something like this:
The idea seems to have been to retain the original Garfield Park El structure west of Sacramento rather than rebuilding everything in the Congress median as was actually done. Maybe the Congress Expressway was originally intended to follow a slightly different route than it actually does, and it was a change in its route that caused the entire Garfield Park branch to be rebuilt as the Congress line.
The plan also calls for a branch of subway that never became part of the El system, connecting the Lake Street El to the Congress at Kedzie. In this drawing I have deleted the line between Kedzie and the Loop, not because the plan actually mentions this, but because there doesn't seem to be any reason to build subway between Congress and Lake unless the intent was to close the eastern part of the Lake line. Keeping two independent train lines open in such close proximity doesn't make a whole lot of sense anyway (though the CTA did it again when it built the Dan Ryan El paralleling the existing Lake/Englewood El for most of its length).
It would not surprise me if, in fact, the intent of this plan was to replace the Loop entirely with subways. The Midway and Dan Ryan lines hadn't been built (or even planned) at this point, so if the Lake Street line was taken off the El and made part of the general west side system, the only trains that would still have been running on the El would be the Evanston Express and Ravenswood lines, both of which were even then only part-time, limited services. Since the Water terminal still existed, it would have been possible to make both of these train lines terminate there rather than on the Loop and to tear the Loop structure down entirely.
In any case, it didn't happen this way. Maybe people were too attached to the Loop to see it go. Maybe it was considered too expensive to build additional subway that would only duplicate existing service that could be maintained for free. Or maybe someone decided it would be seriously unbalanced to have a train line with three branches to the south and only one to the north.