Why do we use encryption modes of operation to convert block ciphers into stream ciphers? Just wondering Why to use encryption modes of operation to convert block ciphers to stream ciphers?
A block cipher in itself can - as the name implies - only transform one block. The ECB mode, which is basically the reapplication of the block cipher for each plaintext - is insecure, as it leaks information about the plaintext. The reason for this is that repetition in the plaintext blocks would lead to repetition in the ciphertext blocks. Block ciphers are deterministic, i.e. given a key and plaintext block as input they will always generate the same output.

So we need to have a mode of operation to convert fewer or more bytes than the block into ciphertext and back again. This mode needs to be non-deterministic. For this reason an Initialization Vector needs to be used. The IV makes sure that we never have the same ciphertext block even when encrypting multiple plaintext messages. We also like the property of the mode of operation to be online: it can process plaintext data when it becomes available, and the data size doesn't need to be known in advance.

There are basically two block modes of operation: ECB and CBC. ECB has already been discussed, it's just the reapplication of the block cipher over consecutive plaintext blocks. CBC uses the IV and then the ciphertext as vector for the next block encryption. As CBC still operates on blocks it cannot handle randomly sized plaintext. For this CBC needs to be paired with either a padding mode of operation or ciphertext stealing. Ciphertext stealing however isn't completely generic; it requires at least one block of plaintext. Padding modes open up the ciphertext to padding oracle attacks. Finally CBC also requires an unpredictable IV.



A stream cipher (mode of operation on a block cipher) has the nice property that it is secure and it can handle single bits or bytes at a time. It is online, which means that it is always ready to process data. Because it operates on bytes it doesn't require a padding mode. They generally just require a unique IV. 

A stream cipher may offer more advantages such as being able to encrypt/decrypt in the middle of the stream, to use the cipher only in encrypt/decrypt mode and to pre-compute the key stream used for encrypting /decrypting the plaintext. Counter mode (CTR or SIC mode, to use a specific term) offers all of these advantages.

So basically we need a block cipher mode of operation to be able to encrypt / decrypt messages of any size and any content without opening ourselves to attack. And stream ciphers have nice properties that make them more applicable / secure for many problems.

CTR mode is used as underlying mode of operation for many AEAD (authenticated cipher modes) because of these properties. CTR mode is part of GCM, CCM and EAX modes of operation and even for SIV (which uses a deterministic IV which doubles as an authentication tag).