If I rarely turn off my phone, are there any benefits to encryption still? If it becomes the case that my phone is stolen, I would like to make it as difficult as possible, if not impossible, for my data to be accessed without my permission. 

I understand that Android has the ability to perform a full disk encryption on my phone. However, I also understand that the disk is decrypted on boot. Which means once the phone has successfully booted, the encryption is no longer applicable.

Personally, I tend to keep my phone booted at all times for convenience reasons. This seems to imply that my phone will therefore be decrypted at all times. Given this situation, are there still any benefits to encrypting my Phone? Additionally, would encryption help me at all in the case of theft? If not, are there any alternatives to protecting my data from theft?
As long as your phone is turned on, no matter if it is locked, in airplane mode, etc., the data partition remains indeed decrypted and therefore, as you say, you do not really take advantage of disk encryption.

Even worse: when I say that the partition is "decrypted", concretely this means that the data encryption key is present somewhere in your phone memory. If the data on your phone is valuable enough (eg. has any value for corporate or governmental adversaries), there are techniques allowing an advanced attacker to dump this memory, get this encryption key, and access your data no matter if your phone was locked in the first place.

The good news is that there are applications allowing you to shutdown or reboot the phone after a few unsuccessful unlock attempts. Concretely, this means that after let's say 5 wrong unlock attempts, the phone will shutdown/reboot, effectively dropping the encryption key from memory, leaving the attacker no way to access your data without finding your encryption key.

Moreover, I attract your attention the fact that Google put an arbitrary limitation in Android requiring the end-users to use the same password for decryption and unlocking. If you have rooted your device, there are ways to use a strong and complex password for disk encryption and a quick to input unlock PIN. Be aware that using short/easy passwords or a PIN for encryption essentially annihilates any advantage brought by encryption since they would be breakable using dictionary or brute-force attacks.