Use of stealth address is optional with Bitcoin and mandatory with Monero.
What are the advantages and disadvantages of mandating the use of stealth addresses?
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The big advantage is that enforcing one time addresses at the protocol level will prevent people from forgetting, or not bothering with using them. In fact, reusing an address in Monero leads to an output becoming unspendable (since two outputs will also have an identical key image).
If the protocol was changed to allow address reuse, it would of course undermine privacy for the parties in that transasction, but it would also undermine privacy for the rest of Monero users in some small way, by making it fractionally easier to make inferences. For instance, if you are trying to work out which if inputs A, B, C, and D is the real input in a transaction, if one of them uses the same address as another input you know is from someone who sold all his monero beforehand (or other arbitrary reason you know they can't have spend an input, as it is irrelevant for the argument), then you can remove that input from consideration. This is similar to how you can remove inputs from consideration if they can be found to be spent with mixin 0 in another transaction, etc.
The main negative of using enforced one time addresses is that it becomes hard to scan for outputs paid to you: you have to process every single output of a transaction with your view key to see if it is yours. This makes SPV wallets difficult, and is generally slow.
Many cryptocurrency users are either uniformed about best privacy practices or too lazy or undisciplined to use them. Automatic stealth addressing adds privacy by unlinkability without requiring any extra thought or effort from users.
Monero stealth addresses also have some synergistic benefits when combined with ring signatures (and soon RingCT) which are not available to work alongside Bitcoin stealth addresses.
In terms of negatives, stealth addresses are the reason why this Monero rich list does not reveal the information Bitcoin users are accustomed to seeing. Monero is private as a default. Auditing Monero accounts is possible with the use of the viewkey and other tools, but it arguably requires more effort than it would with Bitcoin.