I've done some additional research and found out you're right. I found a log of Harry Chapin's itinerary from that time. It shows that July 6th is the first Tonight Show appearance, and as you say he had two subsequent appearances that year. The 'urban legend' you referenced was mentioned in numerous biographies. That doesn't make them right.
In that same log, I found an early April appearance on the Dick Cavett show, and then a return. So perhaps some biographers conflated the two shows. But Cavett was the first national TV appearance. That was timed with the early promotion of the single.
Having said all that, I stand by the rest of my post, that Elektra promotion was under pressure to come up with a hit. They didn't get one for two years. Fifty years later, the song has very limited airplay. About a dozen spins total on 5 stations. The airplay on progressive rock FM stations wasn't charted or documented, but it obviously had some impact on album sales. And they managed to get a Grammy nomination out of it.
Right. If you look at Harry's chart performance, both singles and albums, he had one hit single ("Cat's in the Cradle") and one hit album ("Verities and Balderdash"), driven by that one hit single.
Everything else was a disappointment. Bottom line, and I know a lot of people love the guy---Harry Chapin wasn't commercial. He caught lightning in a bottle with "Cat's in the Cradle" because it touched a nerve in people with parent/kid issues (and the older I get, the more of that I see in life).
"Taxi" was a turntable hit. I promise you, if there were Gavins and Rudmans and Hamiltons available at World Radio History-dot-com for those weeks in 1972 that it was getting Top 40 airplay, you'd see "great phones" a lot.
I was on the air then. People wanted to hear the "weird song about the guy and the girl he knew that he picks up in his cab" (the title couldn't have
BEEN any simpler, and still no one knew what it was at the time). But it didn't translate to big sales of the single or the album.
And yet, we remember it. ChannelFlipper brings it up as an aside to TallGuy and PTBoardOp mentioning "Cat's in the Cradle", and (apart from VChimp), everyone here knows exactly what record we're talking about.
I was going to ask the rhetorical question "What other song from 1972---
51 years ago---that stiffed at #24 do we remember as well?", but let's just haul out Whitburn instead:
Wilson Pickett-Fire and Water
Joey Heatherton-Gone
Isley Brothers-Pop That Thang
Bobby Vinton-Every Day of My Life
Detroit Emeralds-Baby Let Me Take You (In My Arms)
Chicago-Dialogue (Part I and II)
There's only one that I think has the same level of recognition as "Taxi", and I've saved it for last:
Elton John-Levon
That was actually the bigger of the two singles from that album---"Madman Across The Water" ("Tiny Dancer" stiffed at #41). But Elton was able to move albums off those two songs (and others)---"Madman" peaked at #8 and went double platinum---and Harry couldn't.