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I'm not a Bridge player, but I have been reading about the game. This part of the rule surprises me. After the contract is closed, Dummy lays down his/her hand and thereafter doesn't take part in the game anymore.
From a game design perspective this looks silly. It excludes one of the players from the game. Dummy essentially becomes a spectator, which is certainly less fun. If it can't be avoided (e.g. making an incorrect accusation in Cluedo) then yeah, but Bridge offers an obvious way to keep Dummy in the game - just don't have Dummy drop their hand after bidding finishes and play normally.
This isn't for the purpose of excluding the player from the game - and typically the player in that seat will physically move the cards requested by the declarer to be played. The idea is that dummy's hand (and only that hand) becomes public information, creating an asymmetry - the declarer knows all 26 cards that will be used to try to make the contract, but the defenders must infer each others' holdings from the play.
Why create this asymmetry? I can think of two reasons:
It creates strategic depth. In particular, consider finesses. The skill set expected of declarers includes understanding the play of a finesse, as well as being able to determine whether to attempt them (based on conditional probabilities as well as the risk and reward involved according to the scoring system). If dummy's hand is closed, this becomes impossible - one player on the declaring side may intend to lead into a finesse, but the other player won't know this is the intent, and is torn between the priorities of ensuring the trick is won and sending lead-directing play signals. If we instead open one of the defender's hands in addition to dummy's, the play again becomes impossible - since everyone can deduce everyone else's hand, there is no longer a question of risk.
It makes bidding more competitive. Because of the trick-winning advantage inherent in declaring the contract, it's often possible, when the honours are evenly split, for either side to be able to make a 2- or 3-level contract even without unusual suit length. This enhances another skill component: deciding whether a sacrifice contract will be preferable to letting opponents make their game or slam (in rubber bridge, one might even sacrifice against a part-score contract if it would complete opponents' game).
Okay, but why not just reveal dummy's hand to declarer privately? I can think of three reasons:
It would violate a sacred design principle. Players are only supposed to communicate with each other via their actions - including publicly-known codes in bidding (I believe you asked a separate question about this).
It would be mechanically difficult to implement. If declarer only gets to look at the hand once, it creates memory issues; if multiple times, then it involves repeatedly passing cards across the table, which is messy and creates potential for cheating (by swapping cards between declarer's and dummy's hands, which defenders wouldn't know about in this hypothetical).
It would unbalance the advantage created by making it too strong. As is, defenders can take dummy's hand into consideration when choosing leads (except the first) and responses (i.e., avoid playing an unnecessarily high card when declarer is trying to exit with an unavoidable loser). Overly competitive bidding would ruin the scoring system. (While it might be feasible to calibrate that to match, the game was after all developed pretty organically. The current balance works; why disrupt it?)