While that can be done, it IMO is questionably not worth doing over simply adding more optional bosses to the game as a whole, with the same said "new tactics" as your hard mode enemies. Thereby, increasing the size and content of the game on any difficulty setting..
I used new tactics and additional enemies mainly just to give it a sense of freshness. Its kinda like dinner. You don't wanna have the same thing every night so of course you make something new the next night, and so on and so forth.
I can't speak for tales of abyss because I never played it. But that would be an example of a bad situation or example. This is why I mentioned doubling hp and not damage. Doubling your enemy's damage obviously would require the player to just plain do more grinding, because chances are it would make many enemy attacks that are unavoidable 1shot material for a long time, which doesn't increase difficulty so much as increase the player's need to level. However, with the exception of "I'm at 20% health nuke me down in 5 seconds or I cast ****CATAPOCALYPSEE!!!!111one****, increasing hp by significant amounts increases boss difficulty without actually increasing the need for a player to grind more. Of course, there ARE some rpgs where the enemy damage output is gimp by nature, and probably COULD be buffed safely without forcing the player to level more. Anyway, giving the player the option to manipulate all of these, while requiring little more code than global constants in front of each stat would go a long way given the little effort required.
Yeah I figured you never played ToTA. I'll give you some insight on what their difficulty modes did.
You had Normal, Hard, Very Hard, and Unknown(Japan had 5, which included a Mania mode between Hard and Very Hard). On Normal, stats are normalized(1.0x). Hard mode multiplies those stats by 1.5, Very Hard by 2x, and lastly Unknown Mode multiplies the stats by...3.5(Originally 4x in the Japanese version). Now on higher modes it would allow some bosses to use their Mystic Arte(think of it as an ultimate attack). If they used them before, then they might use a different one(IF they have more than one), or reuse them later on in the battle(They usually do them when their HP is at certain points). However this isn't a problem, cause most of them are easily dodgeable(Some are full screen but won't kill, just reduce your HP to 1 at the most).
The first battle I mention is against 1 enemy, and is sort of a tutorial battle. On Unknown mode however, its just an annoyance as its a battle that lasts 10 minutes with you just infinitely wacking the damn thing dealing only 1 HP worth of damage. If your Attack(Or F. Attack, which is kinda like Magic Attack) is less than half the enemies Defense(F. Defense in cases of F. Attack), then you'll only deal 1 Damage per hit, even if you use your character's Mystic Arte. The only good thing about Unknown mode is that it can be played after you give yourself special NG+ Bonuses like 10x more exp and such, but after the first battle you just wanna say "Screw it" and switch to Hard or Very Hard mode.
I'm sure you weren't planning on something like this when you mention buffing stats for higher difficulties(You said it yourself, HP only), but of course this is one example of what not to do. While an HP buff for higher difficulties is a nice touch, attacking a few other new additions wouldn't hurt. Heck not every enemy/boss needs a new attack/tactic, just a few of the more "Smarter" ones.
Have you played valkarie profile 2 btw? (might exist in 1 too). Additional playthrus in that game provide a stat increase to your enemies. It increases the difficulty of the game by a noticeable amount, but makes it fun and fair the whole way thru. The only problem I have with this game is that I don't WANT to have to beat the game 10 times to crank the difficulty into overdrive, if I could simply set it at the start of the game >=).
Never played a VP game, except the one for the DS. I've watched the original and VP2 though at SpeedDemosArchive(I'm..sorta trying to work on getting a Touhou game up on the site but I got no one wanting to be a verifier for Touhouvania x_x). The only thing I find wrong with what you mentioned is that I could have some really powerful equipment from the first playthrough to just blaze through the game even with a stat increase to enemies(Then again, I don't know much on how those 2 work compared to the DS one). If the stat increase is enough to make it so that using such items don't make it so easy to blaze through then that works since it would provide a little difficulty. Not that much if the enemies fight the same since I would just have to kill it the same way as before, just with stat differences.
Any strategy could be valid, but everything depends on context. Personally I like an RPG with a decent amount of RNG in its damage formulas. Like FF 2/4 for example, sometimes you'd smack for 1k, and then you'd thwack the same target for 6k, and crits were NOT involved. But there was definately a clear average. I rather liked this system personally. I believe it was that you did like 500 damage, but you attacked like 15 times, and you had to roll hit/miss for each attack, when you actually selected attack. I think this system is really cool because it makes hit/evasion useful, without forcing the player into experiencing painful miss streaks on a regular basis(attacks that hit for 0 because they ALL missed I mean). However, hit/evasion can be a very bad thing to manipulate the RNG for assuming you have a more traditional hit/miss system. Because simply making the player see "miss" noticeably more often is probably just going to piss them off.
Good thing you're talking about the original FFIV and not The After Years :v That RNG was HORRIBLE.