I get what you're saying, and honestly its all good advice... so you're right... up until the bolded part, where I must disagree... Though not entirely, as you will see by my final statement below.
If a DPS is being punished for DPSing, its not so much bad game design as it is extremely poor foresight, You are literally being punished for just being exceptional at your job, this is absolutely unacceptably terrible. And What does this spell for SMN? They can't just "Stop" their DoTs when a phase push comes close, and if your advice is to stop applying DoTs at an arbitrary % close to phase shift, you're essentially asking a SMN to be even more useless. If a DPS doing their job, and by doing their job I mean everything you mentioned except the bolded part, and you can manage to "Break" the fight and cause an instant-wipe, its poor game design. I shouldn't have to count to 5 between each of my combo buttons just so the last boss in Haukke doesn't Deus Ex Deathga the group.
It is absolutely vital and key to being a good player in general to be aware of Phases, DPS or otherwise, and to know when each is coming up, but theres also Ramuh Extreme which you can (easily) accidentally Phase-Push after someone gets charmed, leaving in the end about 4 charmed folk by the time lightning comes around which could lead to a wipe if people aren't ready. Ramuh EX is already so technical for a primal that its almost universally hated, is having to watch HP for phase pushes really a necessity? - No, its not, and it shouldn't be.
If SE can't have the foresight to design a boss that doesn't "Break" and unavoidably wipe everyone due to an accidental phase push, we're f**ked in the long term as our Item level gets higher and higher, and imposing level caps will just end up killing off the old content. Who wants to be synced to a 110 dungeon to help people progress when our Item level is 300+?
Unless they're bad enough to actually still get hit, how is this a bad thing? Why does this offend you so? Do you get angry at SCH's who throw out one last Adloqium before tank pulls because "They gotta get that one more cure for protection!" even though it could go off too late and they end up getting hate? No, its their frickin' job and it also happens to be a smart thing to do. If you're doing a 3-step combo on DPS and are on your third hit, especially MNK keeping up Greased Lightning, getting that last hit could be a huge thing and so long as you can get away without getting hit, there's nothing wrong with that... and in fact not doing it would be the stupid thing.
And for what its worth, you can go straight to my lodestone, I play Tank, Healer, and DPS... PLD, SMN, SCH, NIN... I'll pick a role for what I'm needed, and when I'm on that job I'll do that job to my fullest capabilities. I'm not punished as a SCH for keeping the tanks HP topped off and applying Adloqium too well... When on PLD, I have means to control my enmity when needed (Sword Oath over Shield Oath for things like Tank swapping) so I don't even have to hold back when stuff like that comes up, and can prepare ahead of time and swap back to Shield.
So, closing thoughts.I get and believe the mark of a good player is to be aware of these fights which have crappy foresight in mechanics and have KO-Phase pushes, and I think as the game stands now, they should be aware of these and restrain themselves from causing a wipe. Any DPS who pushes these phases and causes a wipe cause they're incapable of understanding it, is a bad player. But I also strongly feel this is straight up poor and bad game design and foresight, and should be addressed. A player should not be punished for truly excelling at their jobs function.