I don't think there's any wide modern popularity poll, but here are some older ones.
Results for this poll were given in Weekly Shonen Jump 1993 Issue No. 12 with Chapter 411. Son Gohan – 51,921 votes Son Goku – 51,256 votes Trunks – 29,627 votes Vegeta – 17,383 votes Piccolo – 9,454 votes Kulilin – 7,438 votes Mr. Satan – 1,892 votes Cell – 1,769 votes Bulma – 1,135 votes Dende...
dragonballworld.fandom.com
Goten and Trunks did fine (especially Trunks, although I'm pretty sure they were adding up both Trunks together).
As for why I think it's all Toriyama? Look at the early marketing for Super. Goten and Trunks were pushed as part of the main cast by Toei's promotional material. They also were heavily featured in Toei original episodes/additional scenes, even getting inserted into RoF and getting a multi-parter original story. But that all slowly faded throughout when it became more and more clear Toriyama had no interest in them for his actual stories.
By the time of the ToP, they clearly gave up, getting much less presence in the new opening, little presence in marketing material and the anime itself showed them falling on their backs while kicking (basically, presenting them as completely unskilled fighters).