Ironically, the aspects you described there are exactly what Giroud have been providing at Arsenal. He's technically good and links up well with the players and there have been so many examples of that. Welbeck may perhaps be similar but I'm not really sure if he's better than Giroud. If anything, one can say he only has better workrate and ability to take on players. Regarding Falcao, I doubt he would have been a better move. Sure, he will get the goals for Arsenal but in terms of suiting their style of play, it would probably be out of sync. He's more of a goal poacher than anything else that needs the team to be built around him as opposed to someone who is more of an all-rounder that can combine with the type of players at the club.