No famous composers would want to mimic. Plenty of unknowns can mimic.
Prokofiev Symphony No. 1 is one of the more famous. It mimics Mozart and Haydn (obvious choices!)
Stravinsky’s Octet is another.
There are plenty of other examples. Those are just two of the more obvious ones. Bach did it. Beethoven did it. Mozart did it.
But if some unpublished work mimics a certain style, I would assume that it is an exercise to gain a better understanding of that style.
It was mostly a prank on the music industry, but nonetheless, mimicry of style was involved, and was enough to fool many people for years.
If you listen to Haydn's sonatas, do you feel the resemblance of Mozart's? Well, because Haydn taught both Mozart and Beethoven.
Nothing is new under the sun, my friend.