Not quite "modern" examples since they're from 1997, but the songs from the Sega Saturn game Sonic R (all performed by British singer T.J. Davis) always felt like they were a perfect match for the tone and style of the DiC dub of the anime. They had just that right flavor or cheese and corniness that was also part of the game's charm and appeal.
Ditto HappyMoon Lady Gaga's Venus makes me so think of Sailor Moon. It could honestly be a opening for a Sailor V anime.
Anyways I don't listen to many modern artists even though there are some like Lady Gaga that I love but honestly Catch Me I'm Falling by Pretty Poison sounds like it could be when Princess Serenity first meets Prince Endymion in the past.
Especially the intro part.
I am descending from heaven above
So catch me, I'm falling
Hold on to my love, ooh, oh-oh
Are you ready, boy?
Here I come, catch me, I'm falling