Eyeballing the chart in the OP and the French data shows them to have a comparable pattern. While OP's data is horses per person, and the French is total number of horses, both show a decline in horse numbers starting about 10 years after widespread adoption of the motor vehicle and falling to 50% of their peak in the mid- to late-1950's, with the French data being perhaps a bit over 5 years delayed compared to the US data. That is, it took 25 to 30 years after mass production of automobiles was started by Ford for 50% of "horsepower" to be replaced.
The point isn't to claim that motor vehicles did not replace horses, they obviously did, but that the replacement was less "sudden" than claimed.
Yes, I considered that. Someone using a horse-drawn wagon to deliver goods about town would likely not consider buying a truck until the cart horse needed replacing.
The working life of a horse may be shorter than the realistic lifespan. Searching for "horse depreciation" gives 7 years for a horse under age 12, the prime years for a horse being between 7 and 12 yrs old, depending on what it is used for.
I'm willing to accept the input of someone more knowledgeable about working horses, though!
The point isn't to claim that motor vehicles did not replace horses, they obviously did, but that the replacement was less "sudden" than claimed.