JRPGs are known for bad combat systems (low skill, grind-heavy, time-consuming), but it makes me sad when I see people dismiss the genre for it. Bad combat systems are not inherent to JRPGs anymore than they are to RTS games.
If you define a "JRPG" to be a story game with no player-insert character, as I do, it says nothing about the combat system used in the game. It's purely convention that they're turn-based and poorly designed in numerous ways.
To show this in practice, I wanted to mention an example of a JRPG that tried to improve the traditional combat system model, and made significant progress: Mario and Luigi: Bowser's Inside Story. (Update: main_gi has pointed out that Bowser's Inside Story is not the only game to do this; it's been consistent throughout the Mario RPGs. His guest article is here).
There are numerous things to hate about this game. The tutorials are awful, incredibly patronizing and two-thirds of them are unnecessary, and Starlow's dialog doesn't help. They also introduce so many incessant minigames for story events most of which are only used once or twice (and don't get me started on the Bowser's nose minigame, which is the most absurdly frustrating thing due entirely to the controls being janky). There's also a brute-force skill test (rapid button mashing) that's not needed for most of the game but unfortunately becomes a gatekeeper just for the final boss. Back in the day I could barely do it and had to help my brother. (Though main_gi informs me that even though it tells you to mash X, you can actually mash X and Y at the same time and it makes it much easier.) But the battle system...
It uses basically a typical JRPG battle system with only one big change: manual input during attacks that makes it possible to completely avoid all damage if you're good. Whenever an enemy attacks you, you get the opportunity to pass some timed button press challenge to dodge it. You also get similar inputs on your attacks, giving you a range of something like 4x as much damage from perfect input as you'd get from not pressing anything. It's like Dark Odyssey.
They did a pretty good job with the telegraphs too; the way to dodge was almost always intuitable or reactable, and when it wasn't it usually wasn't a one-hit-kill either.
It's kind of funny, because without the Dark Souls-like input this battle system would be even worse than Lost Odyssey, since most tactical decisions are trivial, whereas Lost Odyssey was at least deep enough to support a surprising amount of strategy.
Honestly, I'd be positively recommending this game if the timing challenges were harder. Unfortunately it's very easy to play close to perfectly. The game doesn't have difficulty settings and the one difficulty that exists is easy, not normal. A lot of the timing challenges that would be tight enough to be interesting have a design flaw that allows you to bypass the difficulty by pressing redundant buttons that aren't punished. For example, there's a boss you fight as Mario and Luigi that has an attack where a group of minions encircle the Bros and fire a few lasers in sequence. By watching their movements closely you can tell who they're going to hit and press the corresponding jump button. The problem is that you can just jump with both Bros every time and it trivializes it.
The story wasn't actually bad if I remember correctly, and the music was never a disappointment either. The final boss music gave me goosebumps the first time I heard it.