Because that doesn't give you security if the site is compromised.
For example, if my Phase+password combination is RootGod+Facebook.com it wouldn't take very long for someone to realize that RootGod+Gmail.com would also likely work there.
I thought that the Password+Site combo assumed the usage of SHA1 or MD5, though I know that this doesn't work for some sites (with max password limits). Maybe CRC32 in those cases?
CRC32 is bad way to hash anything, if you want secure hash of some obscure length, just truncate output of say SHA-256 (by the way, SHA-224 is exactly this: truncated output of SHA-256).
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Why not just use the phrase+password as a password?
Because that doesn't give you security if the site is compromised. For example, if my Phase+password combination is RootGod+Facebook.com it wouldn't take very long for someone to realize that RootGod+Gmail.com would also likely work there.
I thought that the Password+Site combo assumed the usage of SHA1 or MD5, though I know that this doesn't work for some sites (with max password limits). Maybe CRC32 in those cases?
CRC32 is bad way to hash anything, if you want secure hash of some obscure length, just truncate output of say SHA-256 (by the way, SHA-224 is exactly this: truncated output of SHA-256).