It would be great if on the Users > Manage Users > New User section there was a toggle to check off if you would like an email sent to the new user welcoming them and providing their username and password along with a link to the site for convenience.  Doing so would make the process of an admin creating a user a very quick and easy one step process of adding a username and email address and checking that box.

Would that be difficult to do?

No, it wouldn't be hard, and it's crossed my mind as well — a feature we need to add in. To do this, one would:

• Open /core/admin/admin_area_users.php at #225, if (!empty($_POST['new_user']))... This is where a new user is added in the Admin CP.
• Open /core/ajax/members.php at #532 - if ($result > 0)... This is where a new user is added during regular registrations, mailing happens from #575 onwards, if ($core['init']['validation_type'] == "none")... etc. depending on what mode your registrations are in. 
• If you wanted it automatically sent for all new admin-made registrations, you'd just hook in the mailing routine, and if you wanted to choose the event, you'd add a select dropdown into admin_skin_users.php / $skin['admin']['manage_users'] in the new user form, and make the mailing conditional in the admin function accordingly.

Is the code clear enough there so you can lift it out and into the admin version, or would you like me to type this out? If so, I can key the feature in over the weekend — not that complicated.

Keying it in would be great.  I am pretty smart, can reason well, and am fairly persistent which allows me to follow your suggestions for modifications in the code, and often study the code and follow the logic in how pieces fit together, but I am a novice at PHP and so as far as custom coding I would not be able to do it.  (For example, following your guidance for creating the custom admin email notification stretched my limits.)

It is not as crucial a need as the others I have posted here and especially in the Premium Wiccle forum, but an extra feature that would serve my client well, and so certainly appreciated.

Tagged as accepted feature request. It's quick enough to add in, and should be no problem. It'll be easy enough to roll this in with an update to your client's site with the next upgrade release.