Looking at things like Plato's cave, the people trapped in the Matrix (movie trilogy), and Star Trek the original series episode "The Menagerie" as points of reference/ touchstones for the answer(s), I would like to know why do some people want the illusion of good and known vs facing the reality that is.
There is an external world and there is us. Our illusions do not change external world but can change our own state of mind and thus our attitude, behaviour, and responses to situation. Now, if illusion produces a result that makes us more adaptable to our surroundings, then it might be considered to be desirable (pragmatically). A very good and often used example is that if you have fear of speaking in front of large crowds then you must imagine that the room is empty. This lowers your anxiety and thus helps you speak better because your own anxiety was making you less adaptable to the situation (where best thing for you would obviously be to speak). Some would say that this is not exactly going against reality but actually diminishing an irrational and unreal fear by thinking of contrast. Here, I am reminded of Victor Frankl's book, "Man's Search For Meaning". In the second part "Logotherapy in a Nutshell", he talks about antcipatory anxiety. It is according to him counterable by paradoxical intention. It is not exactly creating an illusion though.
The point is in order to remove a fear, best thing would be not to think it. Thinking about it makes you aware of it even more and that causes a viscious cycle of action and reaction (a sort of system with a positive feedback greater than unity) that results in hyper-sensitisation to the problem and thus more severe symptoms. That would require either understanding its extent and not over-reacting or ignoring or thinking of something else, or thinking the event to be something else. Sometimes, the last option is most easy and immediate. However, the illusion may actually cause more problems. Thinking that there is no one in room, you may blurt out something that the audience may not like or is improper, hence ruining everything.
Because our reactions to the world may not always be in a way that best ensure our interests (because of mental factors and the fact that we can think) and the very fact that what is does not mean what ought to be, sometimes it is better pragmatically to artificially produce those responses, by changing the mental factors, that are best according to our needs and interests. Determination of that requires extensive understanding in itself. However, if it is possible then it is an option.
However, if you specifically want to aks why people choose an illusion over reality and not whether and when they should choose it, well that is question related mostly to psychology and not philosophy. Illusions appear real. You have to work to see through them, What would be an incentive for a person to do something which would take away from him what is making him happy? And even if there is some, some people might ignore it if it is not clearly visible to them. It is not surprising that some people refuse to work (apply extra thinking) to make themselves unhappy (or so they feel).
It is pretty difficult to face reality when it is unclear exactly what reality is. Is it what an individual experiences in his own mind? Or must there be concordance with other minds and if so, how many and to what degree? As a practical matter, I believe (if I am permitted to use the term) there must be agreement with other minds if the definition is to encompass their own realities. That may require time, for example, a visionary may arrive at a new conception and others gradually follow.
But your question is why people would prefer an illusion over a posited reality. If you granted for the sake of argument that the reality they rejected was in fact a better approximation of reality, then one might examine why the illusion would be preferred. Humans generally prefer what is familiar to what is novel. There is undoubtedly good evolutionary reason for that, since novel danger might well lurk within a novel environment. Another immediately obvious motivation for preference of illusion over reality would be that the illusion was more satisfactory to the ego needs of the person with that preference, e.g., maybe the illusory world offered a higher self-image or importance to the person. That is simple personality psychology.
Perception by an individual's senses is accurate.
The storage of those perceptions in the subconscious mind is accurate.
The retrieval of that accurate perception is perspectivized as it is brought before your reasoning and logic faculties for analysis and review.
Your 'perspectivized view' is the illusion of which you speak.
Most people rely on their 'perspectivized view' to use in the formulation of decisions for which they anticipate 'stellar' outcomes. Unfortunately, those decisions usually have less-than-stellar outcomes, precisely because a 'perspectivized view' is a view which does not contain as much Truth as an individual's perception provides to the analysis and review process.
Consequently, it is never a desired positioning to take philosophically.
In summary, the accuracy of your perception of an issue is considerably more truthful than the accuracy of your 'perspectivized view' of the selfsame issue, therefore any 'philosopher' worth the moniker would never desire to accept a humanly conceptualized illusion over the reality of their perception.