A personal thought about this, already many people don't know how to safely send a regular string to the database... let alone sending a password. (See Is single quote filtering nonsense? as an example of issues with strings.)
That being said, MYSQL has a PASSWORD() function¹ that you can use to save a password in a string. Pretty close to what you're talking about.
Most languages now have extensions that will hash the password and give you a string to save in the database. They may even have a compare function so you don't have to do much to know whether a password entered by the user is a match.
In terms of security, I think the main issue is that you often open your database without encryption. So hashing the password beforehand is safer. Having encryption on your database connection is also going to slow down the queries. Everything will have to encrypted/decrypted before it gets transferred.
¹ As noted by Gh0stFish, the PASSWORD() function uses SHA1. They also offer a few other functions such as MD5(), SHA1(), and SHA2(), all of which are not considered good enough for password security. For much more about password hashing, I suggest this question and its many answers with many updates: How to securely hash passwords? — I guess this means database systems are slower in adopting new technologies because updating their code is more costly (takes more time to make sure it all works properly) so it's easier and safer to have it in your language (i.e. adding some functions in a language is safe if you don't call said functions so your old code continues to work as expected).