This might be a bit confusing, but "consistency" in CAP doesn't have one "strict" definition. It can be roughly defined as "a request will either return the correct response or return an error", but you'll find that the CAP theorem will apply to different variations of "correct response". There are some super exact definitions where we've formally proved it, but there are also plenty of variations where the theorem "obviously" applies as well.

If your definition of "consistency" is "read will always returns the latest value which is accepted by all nodes in the first phase" you'll always have to contact all nodes when you're reading the data (since as you mentioned you can't actually depend on if it's been "committed"). This is "CP" because you "tolerate" a network partitioning by having the read return an error if it can't reach all nodes.

But you can "tweak" your definition of "consistency" to be "reads will read the latest committed value on that node". CAP still applies for the system as a whole (with writes), but now you can serve fast reads from a single node.

Many systems defines "read consistency" as "snapshot isolation" which means (roughly) that all requests inside a single transaction will be executed against a single snapshot (which possibly isn't the "latest" one). This will also allow you to execute reads against a single node.