Cars last much longer in warmer climates. So you would - and still do -- see much older vehicles in southern California than you would in Idaho, Minnesota or Massachusetts.
15 million Model T's were sold between 1908 and 1927 (when Ford ended production of the Model T and converted lines for production of the Model A)-- and you'd have seen them on the road reasonably often into the 1940s, by which point even if still operable they were functionally pretty much obsolete. Ford continued producing replacement parts including engines for the Model T until 1941; enthusiasts and specialty firms still do so today. Ford itself built six "new" Model T's from warehoused parts in 2002 as part of the 100th anniversary in 2003. There are still thousands of Model T's in operable condition . . . enthusiasts and car clubs keep them going today, so it's really a question of what do you mean by "became obscure"?
There are plenty of photos of American streets available online from different dates-- Model T's are scarce in routine use by the 1950s; but they'd likely have been reasonably common up to the late 1940s-- remember that during WW II, civilian automobile production was significantly reduced as factories were converted to produce war materiel; production returns in a big way in 1948 and 49. Up to that point, between Depression and then the War, people kept the cars that they had going, if they could.
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