I disagree in part.

Someone had to train Darth Maul. That kind of makes it implicit that Palpatine would have a lightsaber and know how to use it. Him having it while he might be a target for Jedi makes perfect sense. It is for defense if attacked. He proves in both battles that he prefers to use the raw power of the dark side.

Yoda trains younglings in the early use of the lightsaber. That means he was once an expert in its use. His method of fighting fits with his size, though not with his age. But I think when you consider what he might have been in his younger days, everything makes sense. What we are seeing in ATOC and ROTS are his last battles, first with his former apprentice and then with the most powerful Sith any Jedi has encounterd for 1000 years. I’m not saying the battles themselves were the best choice, but both characters having lightsabers and being expert in their use fits with their backstory. Even in the OT it makes sense. Palpatine has eliminated the Jedi and has Vader to hunt down any strays they learn of. Yoda is in excile and has more to teach Luke than saber skills. Neither of them has need of their lightsabers at that point.