Tell me, mechanically, the difference between these two scenarios:
- My Fighter swings a sword at a dummy for six hours straight.
- My Fighter engages in bareknuckle brawling, resulting in torn ligaments and shattered bones, for six hours straight, after which he receives healing that fills him back to top shape.
As Pam from The Office would say, "They're exactly the same." Mechanically, that is. You've engaged in six hours of "training" which caused you no lasting harm and cost you nothing. The difference is just how you describe it, no more.
If your DM should grant experience for "training that would make a Navy Seal shriek," he should logically grant experience for any training that has a similar opportunity and resource cost.
So let's take it a step further - what if you remove the healing component, or force the PC to pay for it out of pocket? Okay, let's ask Pam the difference again:
- My Fighter engages in bareknuckle brawling, resulting in torn ligaments and shattered bones, for six hours straight.
- My Fighter stabs himself with a knife, over and over, for six hours straight.
Your verdict, Pam? Exactly the same, you say?
Well, yeah. Because you're just subjecting your PC to random punishment. Again, there's no risk of failure - there's no fear that you'll mess up the trap and get killed, or that the non-lethal spell will accidentally overload and melt your skull. You might as well be stabbing yourself, setting yourself on fire, or hitting yourself with a rock, for all the difference it makes. Randomly abusing your own PC, with no real risk, is not a basis to award XP.
Now, it appears your real question is "Should even the strictest DM award a minimum 1 xp/day?" The RAW answer is "No." Per RAW, the DM only hands out XP for encounters. Now, fact is, the word "encounter" covers a multitude of sins, but sitting around all day and RPing a non-event - and let's be honest, "I train alone all day" is as non-event as you can get, there's no interaction and no real danger of failure at anything - isn't really an "encounter" in most traditional senses.