Here's a comparison of two shots - The left shot's of the first episode from 1969, and the right is from an episode 40 years later, aired in 2009.

But Sazae-san is an anomaly in the anime industry. Given they've churned out an episode (almost) every week for decades now, it makes sense that they'd keep with their existing methods longer than other shows would. "If it ain't broke, don't fix it" type of mentality.
So besides Sazae-san, are there any other shows that ran well into the 2000's with cel animation? If anyone knows of other hand-painted shows that stuck around, I'd like to hear them!