Disagree. Paying more than you think the player is worth immediately just to improve your chance of landing the player is an insane approach that no club with a real budget can afford to take.
Declan Rice isn't some kind of generational talent, like the Mbappe of defensive midfielders. He's a good player and I hope we get him but like anybody else you need to set a limit and be willing to walk away. Because getting Caicedo for 75m, Zubimendi for 50m, or Lavia for 40m is going to be a better deal in the long run for the club than paying some kind of over the odds 100m plus add ons price for Declan Rice.
I think Arsenal have actually played their cards perfectly fine here. Just because you lose the player in the end doesn't mean you made a mistake, as we saw with the Mudryk deal. Sometimes the biggest possible mistake you can make is getting the player at the wrong price.