______________________
Caricature isn't always designed as a mockery. Sometimes it's simply shorthand for something that the target audience sees every day.
Classic Hollywood films, for example, are filled to the brim with Irish cops. That's because, after long decades in which Irish-Americans were deemed the dregs of criminality, some of them began getting into the low-paying but more respectable business of crime prevention. I'm sure a lot of Irish-Americans in the early 20th would have preferred to do jobs other than walk a beat. But life is not fair, and we can't change the past; only understand how the past impacts on the present.
I recall hearing one Indian-American, whose name I did not note, speak on a radio show, saying that, in effect, Apu mirrored his own experience. As I recall, he said that his father immigrated to America as a scientist, but couldn't find work in that department. So he got into motel management, and today, this is still a burgeoning source of employment for Indian-Americans. Again, maybe it wasn't fair that the scientist had to go into motel management. Maybe it was the result of white privilege, maybe it wasn't. But it remains a fact that a lot of Indian-Americans found employment in the management of motels and convenience stores.
I agree that it sucks when Indian-American kids get called "Apu" or have to listen to "Thank you come again." I'm sure it sucked when Chinese-American kids had to listen to "Chinamen" songs and get mocked for being the sons of laundrymen. Yet I think it's unfeasible to say, "We don't like the image of this caricature, no matter whether it represents any aspect of real life or not." I think Hari Kondabolu may be guilty, at the very least, of using too broad a brush to paint his picture of anti-Asian racism.