I think for a good remake, you either need to stay as close as possible or recreate the whole game with current consoles but based on the same old scribbles / plannings.
Anything in-between will make it weird.
Sword of Mana on the GBA (remake of Seiken Densetsu aka Final Fantasy Adventure on the GB) was some in-between. They tried to keep close to the original but altered dungeons and enhanced the story... it didn't feel like the same game, it was weird.
A bad remake. They shouldn't have added that much.
Final Fantasy IV on the NDS was a spot-on remake. The exact same gaming system, same worldmap, same monsters, same everythiing. But with enhanced graphics, enhanced music, etc.
It felt like the same game but upgraded to current tech.
Good remake
Makaitoushi SaGa (Wonderswan Color, remake of SaGa aka Final Fantasy Legend I on GameBoy):
For me, it was one of the best remakes ever. It was the EXACT same game - just with a bit better music and better (colorful!) graphics!
Still very retro, but great!
SaGa 2 (remake for NDS) was not very well done in my opinion: While they kept the original game they added so much more confusing goodies that it wasn't fun anymore.
You may be right:
Games lose the spirit if the remake is not being done by the original team and the new team tries to "improve" it.
Only the original team knows what they wanted to create and can enhance it. A new team could either ONLY enhance graphics and sound or use the original manuscripts, drawings and scribbles and recreate the game completely new.
Everything else will fail.