Since the Internet became widespread, in Romania tens, if not hundreds, of new akathists started to circulate on the web.
Many of them are written in praise of many men and women, not sanctified officially yet, most of them priests, monks and nuns but also common people, which were martyred or brutally tortured by the communist regime of the 20th century for not denouncing their faith and embracing state atheism, for aiding christian dissidents, for opposing destruction of churches etc.
The position of the Church on these akathists is not hostile at all, but rather advising restraint and reading them with great care as although they may be rooted in profound faith and goodwill, many of them contain dogmatic errors, and even biographical errors, not to mention that, although they lived saintly lives, most of these people are not officially sanctified yet.
So, to answer your question, no one in the Church should stop you from writing your own akathists. On the contrary, I'd expect quite the opposite. I'm pretty sure that my father confessor would be thrilled if I would tell him I have such inclinations, unfortunately I don't have the skills needed :)
If you plan to go ahead with this, keep in mind the following:
The akathist has to be dedicated to an officially recognized saint or to Jesus, the Holy Trinity, the Virgin Mary etc.
If you want to publish your akathists (or any writings related to Orthodoxy) in a book approved by the Church (meaning that it will have a prologue containing a blessing by your bishop), it must be verified for dogmatic and biographical consistency. Ask your father confessor where and how to apply for such proofing. (And no, you don't have to be a clergyman to get the blessing from the Church to publish religious writings, there are tons of lay persons out there publishing all kinds of approved Orthodox books).
Don't forget that akathists are prayers. Discuss seriously your intentions with your father confessor, he'll know best how to guide you to achieve the proper spiritual mood needed for such a task.
As for entering liturgical practice, I'm pretty sure that only time and the reader's response will tell. According to the Church's history, the first akathist (of the Theotokos) was written in 626 by Sergius I, Patriarch of Constantinople, and it is widespread throughout the entire Orthodox world. Other akathists are not as widespread and recited in monasteries only. Others, like the ones mentioned above, are widespread throughout Romania only (I'm sure russians, serbs, greeks etc. have similar ones). And finally, many others probably faded away with the passing of time.