what he said ^ ^

Android 4.1.1, not sure how far from stock this is. There's no "contacts" app, but you get the contacts from the dialer. Selecting the contact lets me see photo and name, place a call, send a message or make a video call, if I select by pressing the corner of the contact photo. Pressing on the contact itself shows no menu/contact, but places the call right away. But thank you, thanks to your suggestion now I found out how to do it... from the calls log view. There I can select the contact the same way (corner, same menu), but pressing on the contact doesn't place the call but shows me a detailed menu, where I can delete the contact.  Still an huge UX fail, but thanks! :-)

Definately, in my stock android 4.4.2, its the same as +Duarte Velez Grilo said. But its called "people" not "contacts"

+Gil Gonçalves that. I do have the "people" app, I just saw it... in any case: I add and edit contacts via dialer, but dialer has a similar-but-not-so-featured view on contacts, instead of direct integration with "people"... obviously, this might be better in most recent android versions.

To be fair, trying to delete a contact from the dialer should not be allowed, since the dialer just provides a read only view of your contacts, so I think that's not a ux fail, but a picnic error :D

Oh, but the dialer does not just provide a read only view of my contacts. In fact, most of them were added via dialer...

I just checked and apparently, when you press "Add contact" from the dialer, it invisibly sends you to the "add contact" for the people app

I guess they only added the features that people need from the dialer: See list of contacts / Add new contacts