I think that this sentence's problems start with the deadening and befogging use of passive voice. If I were trying to help readers understand whose interest in researching X is growing, who is investigating its applications to various fields, who has realized the desirability of "X which can directly deal with Y," and who desires it, I would recast much of the sentence in active voice. Because I don't know the various entities behind the growing interest, the investigations, the realization, or the desire, I must guess at their identity in my recast version. Here it is:
Academic interest in researching X has been growing in recent years, as researchers have investigated its application to various fields and as others have recognized the desirability of identifying the ways in which X can directly deal with Y.
By reducing the number of passive terms from four ("has been growing," "have been being investigated," "has been realized," and "is desired") to one ("has been growing"), my revision enables readers to grasp more clearly who is doing what in the sentence. The rewrite also renders the verb tenses simpler and more coherent.