It depends. If you want to just retell stories broadly, only preserving the overall narrative, then no, it's not necessary. But if you want to recite them word for word consistently - which many cultures did and do value - then yes, it requires a lot of rote learning, and learning of various associated memorization techniques.
Thus not all cultures evolved such a distinct profession, but many did. Some particularly impressive examples include the Mongolian Epic of Gesar and the Kyrgyz Epic of Manas. The latter is notable for having over 500,000 lines of verse, and there are living performers capable of reciting the whole thing end to end (which takes several days).
Eh. That comes with a lot of caveats. There's an entire branch to library science (yes, that's a thing) dedicated to storing and analysing different "editions" of the same text because it helps trace how stories spread over time. Usually large parts of the text will be the same but there will be minor changes, often inconsequential, in one edition versus another.
> it requires a lot of rote learning, and learning of various associated memorization techniques
Sure, if you today want to memorize an entire work like that, you will need to do that. But this ignores the historical context. Nowadays you may hear dozens of sophisticated tales every day. You can't even watch the news without hearing narratives, often deliberately constructed to have heroes and villains and story arcs to make boring events sound interesting. Back then, especially in remote villages, your material was much more limited and there was much more work that allowed for telling or listening to stories and songs.
This also ignores the survivorship bias: the people who ended up reciting these stories were likely already interested in memorizing them and found it easier to do so. For example, certain forms of autism literally would have predisposed people to being able to commit such stories to memory and recite them word-for-word, given enough time and opportunities to do so. Telling them in an interesting way then would just have been a craft you'd hone through repetition.
It's also fallacious to think of this as a distinct profession inherently. Without the separation of labor the concept of a "profession" makes little sense even if different people might prefer doing different kinds of work and thus naturally divide some parts of labor without a formal distinction (e.g. in a gift economy it's perfectly plausible for the guy who is really good at making tools to spend more of his time on tools for others who'd in turn take over some of his other work to allow him to focus on that). Yes, at some point memorizing and reciting stories becomes so much work you don't have time for anything else and a culture might recognize that as a distinct profession the same way it might have shamans or holy people, but I'd argue that often oral cultures would strive perfectly fine, even when it comes to longer works.
Now, being able to create such an extensive work and spread it to other groups/tribes/towns is another matter and would indeed be more likely to happen in the presence of a distinct profession. But of course it's no accident that there are so many parallels between historical epics.
Thus not all cultures evolved such a distinct profession, but many did. Some particularly impressive examples include the Mongolian Epic of Gesar and the Kyrgyz Epic of Manas. The latter is notable for having over 500,000 lines of verse, and there are living performers capable of reciting the whole thing end to end (which takes several days).