As if Golden Axe ever had one single good game in the series. People loved them for the simplicity, feel and music. They were godawful in gameplay and blandly repetitive. The recent Golden Axe is the same thing, entertaining for a while, a bad game overall.
I think saying it is a bad game overall is maybe a little too harsh. Repetition could be said about many games at the time, but what kept things fresh was the sense of progression in the difficulty and overall challenge but indeed also in the feel of epicness and music. I don't think we can deny it's seen as a classic in general, its inclusion in allstar racing transformed has mostly drawn positive reactions, but ofcourse there is a lot of nostalgia involved as well.
Altered beast however fits well into your description imo, but then someone else could disagree with me.
SoR is in a completely different level. I really can't imagine the game working with today's videogame mechanics. It would have to be something like Dynamite Deka
I think anything is possible with the right idea/direction.
Edit: Honestly the game doesn't look that bad, just not streets of rage worthy imo