Almost every web service I can imagine has the user pick the password. Why is this? Couldn't the system choose a better password? It doesn't have to be some complicated mess; see this answer.  Do users just find their own choices more convenient? When selecting the password for the user, you know the entropy, as opposed to placing some restrictions that may prevent them from using a low entropy scheme.

Why do we let the user pick the password?

Why, indeed?   

Allow me to ignore that question for a moment, and answer your implied question: Should we?
That is, should we continue to have users create their own password, which is often weak, instead of just having the system generate a strong password for them?   

Well, I am of the controversial opinion that there is a pretty strong trade-off here - having a secure password, and KNOWING how secure it is (as you point out), on the one hand, and on the other side is the user's feeling of security. "Usability", to some extent.  

I think there are several aspects to this feeling of security: some users would want to ensure that they have a strong password themselves (e.g. via a password manager, or diceware); some users would want to select an easy password; and some users want to use the same password everywhere. And yes, many users just plain expect to be able to set their password, for whatever reason - so besides any specific cause, you will still need to fight the re-education battle, which is far from easy.    

Also, don't forget that once you get a good strong password to the user, the (often non-technical) user still needs to figure out what to do with it - even passphrases become difficult to remember after the first dozen or so, or if you only use it every 6 months... The non-technical user would most likely save it in a word document on their desktop, or in their email. (And of course write the OS password on a sticky note attached to the screen). 

Now, don't belittle these reasons, or these causes for using weak passwords - we the security industry have created this scenario for the simple folk over years. But it really comes down to: how secure do you need your site to be. How much risk can the user decide to take upon himself/herself, and how much of that is system risk that should be taken out of the user's hands. 

So bottom line: Yes, I think most sites that have non-negligible security requirements should offer password/passphrase generation. Depending on the profile and architecture, you could offer 3 options when registering an account (or changing password, etc...) - just make sure to only display the password after warning the user against shoulder-surfing:  


Generate passphrase - with a configured or flexible number of words (default)
Generate crazy-strong password with ridiculous entropy, e.g. for saving to password manager
Create your own.   


In fact this is what I've been recommending for some time now (variants dependent on the specific requirements...).    



Going back to your original question, why is the above not done?
I would guess a combination of legacy systems and bad habits; mis-education (the overwhelming majority of sites still have BAD password policies and recommendations); and perhaps just a lack of awareness of a better solution.   

Yes, this is why passwords suck. :-) 
