Are there any asymmetric key encryption/decryption algorithms?
You are mistaken that there aren't any cryptographic standards that describe asymmetric encryption / decryption. You name RSA as an example and then you just show the modular exponentiation. However, in PKCS#1 - the predominant RSA standard - there are methods described to encrypt with a public key and decrypt with the private key. Currently it contains PKCS#1 v1.5 compatible padding (official name RSAES-PKCS1-v1_5) and OAEP (official name RSAES-OAEP). In the standard there are also some links to older standards that these schemes have been derived from.

In principle you can simply split up the blocks and encrypt each block. However, the input block size is indeed smaller than the output block size. Furthermore, modular exponentiation is way too expensive for the private key operation. There is simply not much reason to choose just RSA over hybrid encryption. You could say that you could rearrange the RSA blocks as they always would decrypt even in the wrong order, but AES-CBC doesn't provide any integrity or message authentication either, so I've always seen this as unfair. If you require integrity or message authentication then you'll have to sign the encrypted blocks (or sign before encryption, depending on the use case).

For DSA and therefore ECDSA there is no good encryption method. There is El Gamal encryption, but because the sizes of the keys are relatively small for ECDSA, it is even less efficient than RSA encryption.