Causal inference where potential outcome is somehow "violated"? The fundamental problem of causal inference says that only one potential outcome is observed for each unit.
What happens if both outcomes from control and treatment can be observed? Can we still make use of analysis tools like causal trees to understand heterogeneous treatment effects?
As a concrete example, suppose we are an online search engine and want to better understand how to serve ads. Each time a user enters a search query (request), we pick an ad from a collection of $N$ ads and show it to the user. For each of these $N$ ads, there are 2 versions, one with an image and one without. We randomize users into a control group and a treatment group (same distribution of users in each group), where users in the control group will see ads without an image and users in the treatment group will see ads with an image. By the end of the experiment, for each ad we record the total number of clicks by users in the control group as well as in the treatment group.
In this particular case, each ad is an experimental unit, and we are able to observe outcomes from both the treatment group and the control group. We want to understand if we should add an image to the ads or not.
In addition, each ad has its feature (e.g., associated company, promoted product, etc.), and we want to understand which group of ads will benefit the most from the addition of images. My question is, in such a case, can we follow the routines in treatment effect analysis? If not, what's a more suitable framework?

You misunderstood the definition of unit there. One unit, individual, can not be in the control group and the treatment group at the same time. You can only observe the effect of ONE intervention on an individual, at a given time. The two types of ads in your exemple are the treatment, say A and B, and the visitors to your website are the individuals, the "patients".
In experiments we see all the time what happens to participants of the study in all groups, but we can not see what happened to Bob when he took the pill and when he didn't take it, ceteris paribus(keeping all the rest constant).
This is not an assumption, so you can not violate it. It's a problem, and one way of solving it, maybe, is traveling in time :-) A bit tricky
