Public speaking is certainly expected. Accommodations might be possible for somebody with an obvious and documented disability like muteness, but most people just experience different levels of anxiety which is considered "normal" and something you have to get over. You have to realize the PhD isn't useful on its own; it's just an entry ticket to a community where you will be in continuous collaboration / idea exchange for decades. Really difficult to do that successfully if you have crippling anxiety. It's just not the right fit for everybody.
Full disclosure: I also quit my PhD, for different reasons.
If you were literally unable to give a talk, I suspect accommodations would be made for qualifying exams and thesis defenses; indeed, I would bet this is legally required under the ADA or something similar.
However, giving presentation is an important part of an academic career. As a grad student and postdoc, conferences expand your network beyond people in your lab and department. You might hope that your published work "speaks for itself", but people are people, and putting a face to a name seems to have value above and beyond the intellectual content. Later on, seminars and campus visits are important not only for disseminating your own work and building up a case for tenure, but also establishing collaborations and recruiting future grad students and postdocs to your group.
People certainly make do without giving many talks, but it usually makes things slightly harder and you might need to "hustle" in some other way to compensate: write exceptionally well, lean on colleagues to refer strong students, etc.
But can you just get someone else to give your talks for you? Or, to turn that around, can you make a career out of being another researcher's ghostwriter?
(Yes, presumably, they'd have to understand the subject just as well as you do for the inevitable question period. But maybe you're not bad at private mentoring, just public speaking...)
Full disclosure: I also quit my PhD, for different reasons.