Yes. I'd like that. But you'd need someone
a) with a big back catalogue of different styles or who doesn't mind doing covers or as you say appearing much later in the competition
b) that has a greatest hits album to promote or someone the beeb can actually afford as they are effectively doing A Night With and the filming is a long session
c) that isn't too marmite
d) that can sing well live
e) whose tracks haven't been used multiple times already
Who did you have in mind? 
They did Pitbull week in the States but I don't think he sang live and it was a mix of songs he featured in and his favourite songs. He was a guest judge.
They also did Cher Week and Stevie Wonder week (not singing live though).
It's a big ask. I could imagine a Tina Turner week, a David Bowie week, a Madonna week or a Prince week. They can't use Michael Jackson obvs.
But someone to do a 6 song live set? Elton doesn't need the publicity. We couldn't afford him, Rolling Stones or Ed Sheeran. Best famous name we could last get for Eurovision was bloody Engelbert Humperdinck.
Kylie could do it. Barry for the Fanilows 
Ed Sheeran's not a terrible choice although Sing, Thinking out loud and Perfect have been used already.
I'd dance to Bloodstream - not sure what style.
DWTS Ireland/US have done Icon weeks for a while now.
But I don't know anyone who has had a live singer do a set all the way through - I do like the idea but guess they would be concerned about losing an audience who hate Ed Sheeran or Girls Aloud or whoever - Ed and Elton and Adam Lambert aside, we don't have many national treasures who can knock it out the park.
Will Young!
Still sulking over that. Or another alumnus or a mixture of alumni*
Olly Murs.
Take That.
Conchita Wurst.
(yes tis me under a name change)
and if scraping the barrel then Buck's Fizz. 
Lots of people would miss Lance, Hayley, Tommy though.
- I got it!
Steps, Blue and Saturdays do two live tracks each. Beeb could afford that. Or Heather Small/Mica Paris/Will Young/Faye Tozer/Pixie Lott and Lee Ryan do a song each.
Actually, bring back Ed Sheeran. I saw him in Yesterday and thought fictionalised Evil Ed was a weird cameo choice. Could see why Chris Martin turned it down tbh.