Well as long as they've learned their lesson (and razors edge at least made look like they wanted to attempt to win us back) I'd happily dive back in for a new installment.
I've broken down the big differences between NG1 and NG2 before but briefly the first title was Zelda with violence. It has 3 warm up stages then it throws you into a hub world that is meant to be similar in design to OOT on the N64, you complete dungeons, there's a shop and ultimately you get to run through a final dungeon to fight a few large bosses in a row.
Black was basically a tweaked version of the same game, fine tuning the pacing and adding extra items/weapons and difficulty both higher and lower for new players to try and old players to fight through. It was still pretty much the same game.
Sigma tried to squeeze out as much of the zelda style elements as possible, eliminating back tracking and adding in pointless extra bosses that throw off the pacing (having the odd slower moment isn't horrible hayashi). It also tossed in mandatory stages with Momiji that do nothing more then bog down the entire experience while forcing the player to learn a completely different character. This version was later sloppilly ported to the vita , so if you enjoy 30fps with slowdown instead of locked 60fps then go nuts.
Ninja Gaiden 2 decided on a rethink, the game was clearly more inspired by the NES trilogy. No longer is there a central hub , instead you play through a couple levels in each country much the same as NG1 and 2. Japan, America, Europe,Canada, South America and Hell with a break in the middle for an airship level. It almost feels like at some point in development they were going to let the player choose their stage but eventually they set it up for a more linear path. Combat design is similar to the original game but elements of the "cheapness" found within the NES trilogy have been peppered throughout, enemies that have ranged weaponry constantly pepper the player with damage to encourage the player to keep moving. Combat is much faster and fought against more enemies at a time , using magic isn't as much of a score penalty and is actually quite useful for crowd control. Each region offers up a new weapon for the player to find to add variety throughout the game and each stage also offers the chance to upgrade Ryu. It's as though rather then simply trying his own thing, Itagaki attempted to take the old games and mix them up with ideas from the previous NG as well as competing titles like Devil May Cry.
NGSigma 2 took all of the above and rather then simply fixing the bugs and playtesting some of the bosses a bit more, they neutered Ryu Hayabusa . Seriously this game has no balls. Well, I guess it has bouncing balls held within the fabric of all the various side characters .... who are still jarring and forced pauses scattered throughout the experience. The combat pacing is no longer the high end violent speedy festival of awesome found within the standard game, instead it plays a bit closer to the original title but with all the weapons and perks found in 2. In effect it no longer feels cheap but it also doesn't feel as much fun either. Much like Sigma 1, team ninja made an awful port onto the vita that ... for some reason, tried to add in the NG2 style of combat with all of sigma 2's extras. All in all , it's a strange package that's both better AND worse then the standard game.
Which brings us to the previous installment ... NG3. Someone at Tecmo decided they needed to make a ninja gaiden game more appealing to people that don't play the series. This wasn't just a bad NG entry but it was just a bad game all around. Focusing on it's story and the pathos of being a murderous ninja instead of just making a fun game (and hilariously also still having a terrible plot) , NG3 just ends up being a sloppy mess.
NG3 RE though, fixes many aspects of the gameplay bringing them more in line with the itagaki helmed NG2. It's not perfect because even though the encounters are improved the basic core underneath it all is kind of a mess but it's actually very playable. I'd say it's just below each sigma game overall.
With all that out of the way , I would still like to see a new ninja gaiden game that just takes the elements out of the first 2 games that worked and removes the stuff that did not. If any combat tweaks were to be made I could actually go for something similar to ninja theory's dMc. What I'm referring to is the system of having range/light/normal/heavy weapons on hand at all times. Ryu's normal being the dragon sword , light being the vigoorian flail and heavy being something like diabilaro. Tonfas or sais , nunchakus , the lunar staff , eclipse scythe could all be alternatives in the same catagories. You equip 4 weapons on ryu at a time and can combo them into each other with linking attacks. Take the hub design from ninja gaiden 1 and perhaps offer players a couple of smaller hubs each with a handful of stages to complete within them , possibly with player choice deciding which order to play through the game.
Make levels 45 minutes to an hour with 4 to 6 checkpoints and at least a mid boss and a stage boss. Make sure these bosses are actually fun to fight and not broken. Offer up megaman X style features depending on how you go through levels, maybe killing one boss opens up a different path in another level or makes another boss somewhere else easier ?
Make sure the entire game isn't more then 12 hours in length. Instead the replayability would be more important, offering more variety in terms of play order , weapons used or even difficulty.
The story doesn't matter. Just make sure that there isn't a single moment of the game where you aren't playing as Ryu for any reason. If extra characters are utilized , make it optional DLC that exists outside the main game.