Are there any high-level players who are either known for playing games out until the bitter end or have done so in famous circumstances? Is this considered poor etiquette (I'd imagine it would be rude to force a master to play out a simple king+queen vs. king checkmate)?
To become Grandmaster, you must win many tournament games. They take many hours, sometimes multiple games per day, or many days in a row. Tournaments are exhausting. If you are tired then you make mistakes, and making mistakes means you don't play at the required level to become Grandmaster.
Players who always waste a lot of time by playing on until checkmate instead of resting aren't very likely to become Grandmaster.
Sometimes the grandmasters will play out the K+B+N vs K endgame, so as to have their opponent 'prove' they are capable of carrying out the somewhat tricky mate.
As it turns out, it may be worth playing to the bitter end in this case. There are some examples of even grandmasters failing to deliver the checkmate! Here's a recently semi-famous one from a game played during womens FIDE Grand Prix tournament in Geneva, 2013. Showing only the relevant part; whole game can be replayed here: http://www.chessgames.com/perl/chessgame?gid=1716505
Note: At the time of the game, Anna Ushenina was Women's World Champion!
[White "Anna Ushenina"] [Black "Olga Girya"] [fen "8/8/8/8/B7/2NK4/8/k7 w - - 0 1"] 1. Nd1 Ka2 2. Bc2 Ka1 3. Kc3 Ka2 4. Bb3+ Ka1 5. Ne3 Kb1 6. Nc2 Kc1 7. Ba2 Kd1 8. Nd4 Ke1 9. Kd3 Kf2 10. Bd5 Kg3 11. Ke3 Kg4 12. Be4 Kg5 13. Kf3 Kf6 14. Kf4 Kg7 15. Kg5 Kf7 16. Kf5 Kg7 17. Bd5 Kh6 18. Ne6 Kh7 19. Kf6 Kg8 20. Nf4+ Kh8 21. Be4 Kg8 22. Nh3 Kh8 23. Ng5 Kg8 24. Nf7 Kf8 25. Bh7 Ke8 26. Bf5 Kf8 27. Nh6 Ke8 28. Nf7 Kf8 29. Ne5 Kg8 30. Ng6 Kh7 31. Be6 Kh6 32. Bg8 Kh5 33. Ne5 Kh4 34. Kf5 Kg3 35. Bc4 Kf2 36. Kf4 Ke1 37. Ke3 Kd1 38. Bd3 Kc1 39. Nc4 Kd1 40. Nb6 Kc1 41. Na4 Kd1 42. Be4 Kc1 43. Bd3 Kd1 44. Nb2+ Kc1 45. Nc4 Kd1 46. Bg6 Kc1 47. Bf5 Kd1 48. Nb6 Kc1 49. Na4 Kd1 50. Nb2+ Kc1 51. Nc4 Kd1 52. Kd3 Kc1 53. Kc3 Kd1 54. Bd3 1/2-1/2
Only in exceptional cases, a grandmaster plays until the mate. If the mate is beautiful, or if he is very angry about himself, or just as a joke. But normally, they rather resign one move before mate than being checkmated.
In many cases, grandmasters resign too early, with only a pawn down at a full board or with a bad piece. Nakamura often plays games out, but he resigns in totally hopeless positions.
In short, a grandmaster is rarely checkmated. And I am pretty sure, that there is no master ALWAYS playing to the mate, unless perhaps in a blitz or lightning game.
Here is an example of a master playing on 2 queens down in the British Championship http://streathambrixtonchess.blogspot.co.uk/2010/01/ray-could-play-iv.html