They helped bridge the gap between punk and new wave. They have four entries on Rolling Stone's top 500 albums of all time. They led to Radiohead's current name. They have a big suit. So it's hard to claim Talking Heads aren't important. I'd understand if the band's differences have caused their absence, but if we get past that, there's plenty of suitable songs. Such as...
Don't Worry About the Government
Found a Job
Thank You for Sending Me an Angel
Girlfriend Is Better
And She Was
Wild Wild Life
Life During Wartime
Girlfriend is Better
And, of course, the big hits-
Burning Down The House
So there's 15 worthwhile songs. They've got a few great songs that aren't suitable (too repetitive, piano-driven, what have you), but surely one of these would make a good addition to the lineup.