precedent for curved blade lightsabers?

[cheshire]

[vanir]

It was easier to draw a curved blade from horseback. They're actually very unwieldy to use, centre of mass winds up being in the air behind your wrist and it very much strains it. Straight blades are much easier to use.

Early katana ancestors were straight bladed (8-12th century), early on the classical katanas of the 14-16th century (japanese call them something else, forgot name) were very curved and quite long, for use on horseback. A backup weapon (beginning the daisho tradition) was carried for use on foot.
You're about as likely to cut yourself as an enemy, I've used a few and they're real awkward and very hard to get a good hit out of on foot and extremely heavy on your wrists (there are specific training rituals to help strengthen them, but it doesn't change the fact), you'd want to be slashing from horseback at speed and use the vehicle momentum for effect.
On the plus side just a lateral hack without much skill still causes the blade to slide along the target because of the curvature, thereby slicing rather than chopping, so doing more lethal damage.
If on horseback, they're stupid-proof. If on foot you toss it and draw something else, a handful of rocks is probably better.

The traditional katanas we're all familiar with (16-19th century) are later period weapons designed for use on foot. The daisho was worn only as a traditional symbol of authority at this stage.
Their curvature is fairly slight and solely so that you can have a longer offensive reach but still draw the weapon comfortably. Reach can mean a lot in melee combat. They're still unwieldy and hard on your wrist because of the curve, but not nearly as bad as the precursor type.
There is a particular cutting technique used for these and straight bladed swords by samurai (many samurai preferred a shorter straight bladed sword popularised in media as the ninjato but this refers in fact to another weapon, they are still called katana).
In order to get the slice effect rather than messy hacking, you make contact with the tip of the blade and then use body mechanics to slide the weapon through the cut with increasing force. Hence almost all kendo attacks represent lunging blows (but are philosophical forms, samurai didn't actually fight like you do in kendo, they used budoka and there's maybe 3 schools of it still around since the middle ages, only found regionally in japan and kind of exclusive with membership).

You can still get traditionally forged katana type swords custom made for you today, there's two notable weaponsmiths in Japan from memory, it costs up to around ten grand. The sword is made for you by your arm length and degree of curvature, those two things decide how long it can be and still drawn on foot. One for horseback can be more curved because you don't use it on foot, so it can be roughly six inches longer than someone your height could normally wield.

That's why the curved blades.
You can also see the same lines with European blades. Ones designed for use from horseback are more curved. In this case it was just easier to draw them over a mount.
But they are much, much harder to control on foot, when you're the one providing impetus and direction, mostly on your wrists.

You can tell at a glance when looking at katanas what their style and intended purpose is. If very curved it's in the 14th century horseback style, if only gently curved it is 16th century foot style, a straight bladed one could be from either period and you'll have to look at its construction and markings (will be etched on the tang).
Very well made swords were kept for generations however, periodically re-handled to suit period fashion or utility.

It should be noted that damascus sabres made in Turkey and the Middle East are considered equivalent in quality to late period katanas by archaeological metallurgists. These style of blade is designed to be used from horseback or foot, primarily horseback and is swung in a whipping motion (not like the fencing you see on the movies at all, but sort of like the twirling whipping action you see in black and white epic films, especially Russian ones).

Broadswords of the mediaeval period are designed to be wielded like an oversized axe. You hack and spears were universally regarded as more effective in combat (the reach thing and the fact a sword is actually an extremely unwieldy type of weapon with very very limited use, traditionally they were only ever sidearms, like a pistol where a spear is a rifle).

Musashi infamously used a wooden bokken in unarmoured combat mostly, he was much more effective with that than a gigantic hunk of metal.

[vanir]

Put simply the SW equivalent of the curved blade sabre is the adjustable length lightsabre. It accomplishes the same purpose technologically: offensive reach.
Curved blades were actually a compromise on handling to achieve reach, but they meant you had to be burly even with a long handle and two hand use. I can't overstate how bad they are on your wrist, mine still hurt just thinking about it.

[garhkal]

Tell that to the Ghurkas!
_________________
Confucious sayeth, don't wash cat while drunk!

[Drop Bear]

The first Japanese Swords had strait blades and where called Ken (Lit. Blade), the direct ancestor to the Katana was the Tachi, it was a curved Calvary Sword and continued in use and development through much of the life of the Classical Katana (the Katana was developed to be a footman's Tachi originally), in later centuries a Katana that could be used both mounted and on foot was developed but the Tachi stayed that little bit better for use by mounted troops so remained in use if only in small numbers by dedicated Calvary troops.

[Drop Bear]

[vanir]