Seriously, if there was a point within those quotes, I missed it. Honestly. The fact that several different people have stated that their ship is the best in the fleet rings as about as true as when my managers give the pep talk that our staff is the best in the chain. It sounds nice, is a great morale booster and all, but ultimately is fluff.
So the Borg and Spock a Vulcan are lying or mistaken also? And everyone else is wrong? Come on...

We're in Star Trek Canon 101 territory now, are we really going to argue about whether the Enterprise-D is the best ship in the fleet?
Best of Both Worlds pt 1
BORG: Captain Jean Luc Picard, you lead the
strongest ship of the Federation fleet. You speak for your people.
Flagship: the best or most important thing owned or produced by a particular organization
TNG "The High Ground"
FINN: I need someone better. I heard you were with the
Federation flagship and I knew you had to be.
TNG "Chain of Command pt 1"
MADRED: Why you, of course. Picard. Jean-Luc. Serial number SP dash nine three seven dash two one five. Son of Maurice and Yvette Picard. Born in La Barre, France. Formerly Captain of the Stargazer, where you conducted extensive studies on theta-band subspace carrier waves. Don't look so surprised. How could we have designed a lure for the Captain of the
Federation flagship unless we knew something about his background.
TNG "The Drumhead"
SATIE: Of course he did. Do you think J'Dan could have come on board the
flagship of the Federation and accomplished what he did without help from within?
TNG "Ensign Ro"
PICARD: After what happened on Garon Two, she has no business serving on any starship, let alone
the flagship, my ship.
TNG "Man of the People"
ALKAR: I am grateful for the Federation's offer to escort me, but if I arrive at Rekag-Seronia on board the Enterprise, the armed
flagship of Starfleet, my mission as negotiator of peace will be compromised. There must be a Federation transport ship somewhere in the area that could take me there.
TNG "Parellels"
NADOR [on viewscreen]: We were wondering the same thing about you, Captain. Why would
Starfleet's flagship want to venture so close to the Cardassian border?
TNG "Starship Mine"
HUTCH: I also hear that you're a musician. I certainly hope you'll play something for us. It's not often we get to entertain the command crew of
the flagship. Oh, and speaking of command. Hello, Captain Picard.
TNG "Force of Nature"
LAFORGE: You might say that. This is
the flagship. We should be better than everybody else.
DS9 "Bar Association"
ODO: I know these incidents are the exception rather than the rule, but if security breaches like these could happen on
the flagship of the Federation, imagine the difficulty of maintaining security at an open port such as DS Nine.
TNG "The lcarus Factor"
PICARD: I don't know, and if you're asking me what I think you should do, I don't know that either. I can spell out for you, albeit crudely, what you are choosing between. As the First Officer of the Enterprise you have a position of distinction, prestige, even glamour of a sort. You are the second in command of
Starfleet's flagship, but still second in command. Your promotion will transfer you to a relatively insignificant ship in an obscure corner of the galaxy> But it will be your ship, and being who you are, it will soon be vibrant with your authority, your style, your vision. You know, there really is no substitute for holding the reins.
TNG "Sarek"
PERRIN: These quarters are quite comfortable. The Ambassador and I were very pleased when we heard that the negotiations were going to take place aboard
the flagship of the Federation.
TNG "Remember Me"
CRUSHER: It's all perfectly logical to you, isn't it? The two of us roaming about the galaxy in the
flagship of the Federation. No crew at all.
Star Trek Generations
PICARD: They're just trying to decide whether a twenty year-old Klingon Bird-of-Prey can be a match for
the Federation flagship.
Is watering down all of the technology we see in the 24th century really going to be a valid strategy to justify what we see in Star Trek Discovery? If it is, I would submit that as evidence that Star Trek Discovery invalidates itself from the Prime timeline if that's what its affect is going to be on Star Trek canon. It's simply more trouble than it's worth.