Why is the action fast-paced in Act 2 of The Taming of the Shrew?
The action in Act II of Shakespeare's The Taming of the Shrewis fast-paced to match the events which are occurring with Petruchio, Gremio and Hortensio, and Baptista.
Petruchio is "wooing" Kate as quickly as he can so he can get the marriage arranged and some money in his badly depleted coffers. He has no intention of winning her heart; he simply lays the groundwork for his cunning plan to tame his future wife. A quick burst of activity which leaves her flustered is just the start he wants for his scheme.
The idea that the beautiful Bianca may soon be eligible to wed prompts Gremio and Hortensio to even greater action. The two men are making plans quickly because they're in a race to win the hand of Bianca--and it seems to me they are probably as in love with this rivalry and the race as they are with Bianca.
Baptista moves quickly for one reason--he's afraid no one else will ever want his eldest, Kate, so he needs to take advantage of this opportunity as quickly as possible.
The simplest answer to your question is that quick action, a fast pace, is a key component in a Comedy. It is the potential mix-ups, mistaken identities, and fast, witty banter that make a Comedy funny. Shakespeare makes this even more possible in Act II, by having it be one long scene without break.
Act Two seals the engagements of both Kate (to Petruchio) and Bianca (to Lucentio...though it is Tranio pretending to be Lucentio who "wins" her hand. Meanwhile, Bianca has fallen in love with the right Lucentio, disguised as Cambio.) And these events happen quickly because, as the audience, we aren't meant to sit and ponder the logic of the events, just enjoy the speed and chaos that swirls about, complicating the action.
This makes the happy ending of the play and the marriages that ensue, all the more fun. When all the knots and comic entanglements have been unravelled, the audience is as relieved as the characters at the tranquil "happy" ending.