Considering the quality of music in many parishes, I might consider deafness to be desirable rather than a handicap. But I digress (without even getting started no less).
The problem is: Giving deaf people captions written in English is not giving them captioning in their own language.
American Sign Language, despite its use in America, is not English. It has different grammar and different vocabulary. It may have certain loan elements from English, just as English has loan elements from French and German and Latin and Greek, but it is not English any more than English is one of its cognate languages.
and whether a deaf-mute man could be a priest since the sacraments involve the spoken word.
Ed touches on the subject of ministering to the deaf, which touches close to home here. I have (unsuccessfully) lobbied for some "changes" to the Mass for my blind son. I asked the liturgy committee if the bell could be rung during the consecration (yes I also had ulterior motives) so the blind would be drawn to the moment of consecration. I was rebuffed with the explanation that my son was sharp enough to know that from hearing the words of consecration. Sadly I can say with both the sense of sight and hearing, I still can struggle to focus during that time. I can only imagine how difficult it would be for those lacking the visual of the body and blood being raised.
There is not going to be perfection in this fallen world, but I can't help but think if the Mass were celebrated as the Church has put forth, it would be about as close to perfection as our humanity could attain (that may seem like a no-brainer to most, but go with the thought here.) With the spoken word, the tolling of the chimes, the elevation of the body and blood and the genuflection; even those with limited senses could still understand the significance of the moment of consecration.