It's not a problem that your argument isn't valid. The problem is that you're assuming that you have a full competent team. In solo play there are play-styles that are more rewarding to the player than others. The problem with the phlog is that it punishes people for trying to fight pyro, while rewarding the pyro for w+m1. As I like to say M1 wins kills, m2 wins games. Assuming you have a team that is competent enough to properly use pyro and face pyro; the phlog is underwhelming. However people don't understand kiting, positioning, and cooperation within a team. In a solo scenario the player only cares about what he/she is doing. It's the same reason why pocket medics exist. Players are selfish. Medic doesn't want to heal scout he barely gets any points compared to the heavy mowing the enemy team. With pyro why use m2 when it doesn't directly get kills.(Obviously I disagree with that statement but that's the commonplace for most pyros.) The problem is that you can sit at their spawn and get free kills. You will never have to back because of your free health and your enemy can't stay back far enough for them not to be crit to death. The only counter play to phlog is to stay away from phlog. Also please don't try to argue that you can "run away" from the pyro that you clearly see taunt. Most of the time They come out of nowhere and rush your team with crits and only the scout and medic can back peddle fast enough to not get instantly burned to smithereens, and that's assuming he doesn't rush spawn where you can't leave now for a valuable few seconds.
The degreaser was basically a go-to upgrade to the flamethrower. It implemented "combo" type play style that made pyros feel skillful for properly using their other weapons and spacing. My problem still stands that the airblast nerf hits where it counts for me, because m2 wins games. However I can understand why it needed to have that nerf.
The jag needed the nerf it was a direct upgrade. It's barely noticeable to a competent engie. Plus it does it's job of a quick set up for aggressive play or fast defenses.
Demoknights are annoying. They are a less stealthy, less skilled spy. However as I like to continue to point out to people, the zatoichi now overheals in exchange for crits. The crits were stupid and I won't miss em. Now I feel rewarded for using the zatoichi well enough that I can go on a 10 kill streak and still be over healed. it's not as "nerfed" as people say because now it's not a luck based weapon.
Medics needed those buffs.
And for your last point. I love that feature being added. I like feeling rewarded for helping my team. Unfortunately not many people like to help others and prefer to go on killing rampages. You can lead a horse to water but you can't make them drink, or in this case heal and refund cooldown. It comes down to the competence of the people you're playing with.
Overall I agree with you it's a pretty good update, but it's too difficult to forgive glaring balance issues. The phlog is too strong for solo play. Heavy is one of the most underwhelming classes and he never gets any attention by the valve gods. He still has no reliable mobility, no real utility for teamplay, and no ranged options available for his kit. Engineers keep getting nerfs to items that only skilled engies used anyways. Pyro got unnecessary buffs to ranged damage(encouraging w+m1) and of course the nightmare to face that is the phlog. Assuming you're a rational player you can at least understand why the community is outraged by the changes.