True Pacifist isn't a perfect ending, but it doesn't mean it's not happy at all.
Starting off with, Undertale is a game of choices. There's probably not an indeed "true" ending, despite the names this fandom gave to them so far. And since what changes the fate of that world is up to us, we pretty much not only have the power to decide that, but we also have control in the protagonist.
Frisk isn't necessarily told to save all monsters just because their name is only revealed at the end of TP and because Flowey refers to them as a separate character from the player's hands. And speaking of, the reason why Flowey tells us to leave that world alone, to let Frisk live their life, is simple:
The choice is still ours.
Of course, there's also this speculation that Flowey was actually referring to the first human and not to the player, but think about it. Frisk has the most DETERMINATION compared to Flowey, but we, as players, are the ones who mostly control what they do. We can make Frisk RESET, SAVE, LOAD, etc etc. "But then why is Frisk mentioned by Flowey as a separate character from the player's hands at the end of the route?" Another simple answer:
We are still in the Underground. There's no SAVE point in that cliff on the Surface, and we can continue from its end technically STILL down Underground. It seems like the most clear reason to this is that the Underground and the Surface (the "outside world", the "world above") are both separate worlds. We, as players, don't actually leave the Underground. But Frisk does, if WE let them be without making them RESET the SAVE files still Underground as well as, of course, the entire timeline.
Flowey says that resetting everything again would wipe his memories. Why does he tells us that, anyways? Maybe because of all the battle in his real form, maybe because he harmed us, maybe because he thinks he deserves to be alone and let everyone else with that ending. Of course, regardless of whether he lost his compassion again or not. If we RESET, Flowey will just hurt us all over again, and then WE would be technically ruining him again by making he go back trying to kill us. Yes, Asriel becomes Flowey in the TP ending anyways, but he didn't forget what he did while Asriel Dreemurr. Giving us one from the many lessons of this game:
Accepting things as they are.
You see, Toby said that he wouldn't do any direct sequel to Undertale (and of course, Deltarune is not a sequel). Then, some time later, he said that if the people in Undertale are happy, they will remain that way (addressing about what kind of game Deltarune is supposed to be). However, he said "if", and the lesson of accepting the ending as it is, despite not being a "perfect ending", is at hand.
If the True Pacifist ending is not a "happy ending", then the Genocide ending is no different. Rather, it's far worse. "Mercy from life"? What? I don't think this is what monsters fight so hard for. I don't think "mercy from life" is the basis of every monster's hopes and dreams. And believe me, this is important to note.
Why won't Asriel/Flowey want to be SAVED at the end of a True Pacifist? Because of the lesson of accepting. Why would Flowey tell us to leave the world as it is at the end of a True Pacifist, letting Frisk and their friends living in the Surface in peace? Because of the lesson of accepting. I often see people who do not accept the fact that Asriel/Flowey isn't SAVED in the end of a True Pacifist (or rather, in any route) without thinking about it and just questioning it. And please, Flowey won't regain control of the timeline if the player leaves because of two reasons, like I said before:
Frisk is still the one with the most DETERMINATION, even though we are the ones controlling them; and because the game doesn't actually progress to the Surface, at least not by the lead of the player. (And don't take me wrong, I just meant that, in the Surface, the player can't control Frisk, neither the timeline. We pretty much just press [Z] to read dialogues of the characters on the cliff facing the sunset, not unlike, in a Genocide Route, we just press [Z] to kill Asgore and Flowey, and to talk to the first human. The player is still the one who has the choice to lead that world to the True Pacifist ending, as well as leading the world to the Genocide ending.)
Also, uh... no offense, but... you don't trust Flowey, even though Flowey is Asriel? Even if Flowey seem to have learned something at the end of a TP after all those times and regaining his compassion once? Even if, deep inside, Flowey is tired of being a flower? Not even in a Genocide ending where the essence of Asriel shows all off at Flowey's face? I'm starting to suppose you have this whole opinion because you don't like Flowey. Sorry if I'm being a little harsh, but it had to be said.
"Asriel isn't suffering as a flower anymore" except that now he will never have the chance to take his true form again, neither the chance to feel compassion and love. Rather, he would feel much less than that something Flowey could afford to feel, because he'd be dead. Say, isn't that suffering?
"That power. I know that power. That's the power you were fighting to stop, wasn't it? The power that I wanted to use. But now, the idea of resetting everything... I... I don't think I could do it all again. Not after that."
"Not after that" refers to the battle against Asriel Dreemurr.
But still, YOU still have the choice. YOU are controlling the being with literal most DETERMINATION in the whole Underground, be it True Pacifist, Neutral or Genocide.
'My "human soul." My "determination." They were not mine, but YOURS.'
Not to mention that your actions in Genocide are technically teaching the first human something. Want proof?
"You. With your guidance. I realized the purpose of my reincarnation. Power. Together, we eradicated the enemy and became strong."
However...
"You and I are not the same, are we? This SOUL resonates with a strange feeling. There is a reason you continue to recreate this world. There is a reason you continue to destroy it. You are wracked with a perverted sentimentality." [...] "I feel obligated to suggest. Should you choose to create this world once more. Another path would be better suited."
Another path, huh? What would this path be? Maybe one path where you don't kill anyone in your way, leading the first human to take their reincarnation for destruction and then erase the whole world because of what YOU did? Yes, yes, Soulless Pacifist. But who did start all the thread anyways? Also:
"Interesting. You want to go back. You want to go back to the world you destroyed. It was you who pushed everything to its edge. It was you who led the world to its destruction. But you cannot accept it. You think you are above consequences."
Adding their statement that you never were the one in control, adding the fact that you've made they adopt this vision and conclusions at all. In fact, the True Pacifist ending is only unhappy if it is the Soulless Pacifist. Undertale doesn't have a perfect ending, and was designed not to have.
To finally close this long text, keep in mind that, despite everything, both Asriel and Chara are still children. And children have a lot to learn during their life, right? The protagonist is no exception. And, to be fair, many of us are no exception. And by saying so, I not only refer to the essence of the game, the choices that it grant to us and the lessons it can give, but, you know, maybe to our own lives as well. Sure, Asriel and Chara died, Asriel was reborn as a flower, but this will never wipe out the fact that they are still kids.