It's not really good English grammar. It does feel awkward, as has been noted. That's the giveaway, to a native speaker.
And of course nothing like this is treated in school grammars, because they're still talking about English as if it were Latin, with six tenses, two voices, three or four cases, and all sorts of other zombie phenomena. This educational deficiency afflicts both native speakers in Anglophone education, and foreign learners in ESL classes worldwide.
The reason it's ungrammatical is that it runs afoul of what Haj Ross called the Doubl-ing Constraint in his paper on the subject. (Unfortunately, ERIC doesn't have the full text of the paper available, for some bureaucratic reasons, but the link shows the abstract.)
The gist of this constraint is that under certain circumstances (which the paper spells out in detail), one can't use two present participles (-ing forms of a verb) together, with one governing the other.
I.e, the following are just out:
- *Bill has been trying opening the door for a while.
- *I advise watching painting the porch.
Even though comparable sentences without double -ing are fine:
- Bill has been trying to open the door for a while.
- Bill tried opening the door for a while.
- I advise watching (them) painting the porch.
- I'm gonna watch (them) painting the porch this time and see.
There is a lot of speculation about how and why this rule operates, but mostly it seems it just interferes with the parsing routines of many native speakers; i.e, it's a purely syntactic rule, totally unconscious and automatic, concerned solely with form, not meaning.
During my English course I was told that the present perfect tense and the present perfect continuous tense can be used interchangeably in many situations, and it appears to be one of them. However, there is a subtle difference: #1 focuses more on the very activity of working, whereas #2 concentrates on the state (i.e. a job). Therefore, it would probably be more justified to use #1 when talking about a person who carries the same task on and on, endlessly (the Danaides? Sisyphus?); and #2 is somewhat closer to "I have been employed here for 20 years." Still, I am not a native speaker of English ang my arguments may prove wrong.
Best Answer
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.