On a desktop environment, typically the usage of carousels have been as explained by you in your wireframe, i.e. clicking left arrow brings left elements in pushing right elements out and vice versa.
This is not just because of a dominant convention due to the fact that someone started this and everyone followed and nobody dares to challenge or change it now. Infact, Apple introduced this behavior and with the new OSX, they have themselves reversed the paradigm, so now scrolling left moves all content left and vice versa.
The earlier convention has another aspect to it which is related to attention and focus area of the user. This started mainly for a mouse based interaction, wherein user is pointing their mouse to particular locations of the screen to click and make the carousel move left or right. Cognitively, when he/she does that action, their attention, focus and vision too moves to a particular location of the screen, i.e. towards the left or right arrows/buttons. Given this and considering their peripheral vision, it made most sense to scroll the content right on pressing left and vice versa. When the user is clicking left button and content from left is pulled in thereby pushing existing content to right, it is easier for the user to look at the new element without moving their focus by simply using their peripheral vision, as opposed to moving the vision/focus to other extreme of the carousel. This especially played an important role when there is lot of content and user is continuously scrolling in a direction, i.e. lets say there are 10 elements in the carousel and the current position is such that 4th or later content is visible on the carousel with 3 or more hidden towards left. When user moves their vision to left arrow and starts scrolling, they could keep their focus on this area and using peripheral vision keep scrolling and scanning each of the appearing content to find the one they are looking for.
This paradigm changed drastically and reversed in case of touch based mobiles where user interaction were not pointer based but flick based. Since there was no pointer or button involved, there was no such requirement to consider moving the focus area to a particular location of screen to take the action to scroll. Rather user could flick left or right anywhere inside the carousel region to scroll. So instead of a particular left/right region the whole carousel became focus area. In this case, it seemed more natural to treat the carousel as a real world where if you move your vision towards left, you see what is on left and vice versa.
Apple introduced this paradigm shift with iOS and later continued it to OSX. It worked in OSX too with the introduction of multi-touch interactions on the trackpad such that user doesnt need to use a particular region of trackpad to scroll (like conventional PC based trackpads) but can use two fingers to scroll by flicking/moving two fingers together on any region of the trackpad.
If one will notice, even today in phones as well as desktop/laptops or tablets, both type of interaction paradigms are used. There are button based carousels to press left/right button/arrow/graphic on the edges of carousel to scroll and also implicit scrollbar based carousels where user scrolls by using horizontal scroll or trackpad or mouse-wheel. In the first case, no matter which platform it is used on, the behavior is same - clicking left pulls content from left in. Whereas in the second case, given the penetration of touch based devices in our lives, the 2nd paradigm is gaining prominence. This is exactly because of the vision/focus/attention context explained above.
Hope this clarifies the question.