Nintendo have put themselves in a bit of a rut. There are so many different gameplay mechanics, artstyles, and storytelling methods across the various games that it's impossible to please everyone. There is no consistency within the series. I'd go so far as disagree with you about the consistency of the first three games. Yes, there were quite a bit of secrets to discover in the original three titles, but Zelda II's gameplay differences were a larger distinguishing factor and more important in creating a specific niche for that game than the elements that carried over from The Legend of Zelda.
This will always be a conversation topic for Zelda players as Nintendo likes to throw a complete curveball every few years, and as you stated, the series creators constantly throw around the phrase that the next game will be a complete reinvention of the series. I won't go into too much detail about that nebulous claim here although I do believe that creating such standards of hype for upcoming games only causes frustration upon release. The last few Zelda games, especially, have been alienating to large portions of the fanbase.
The thing is, the constant critical success of the series gives the developers more leeway in taking risks and continuing to experiment with the defining characteristics of the Zelda formula so to speak. The commercial side of things is a bit blurrier since Nintendo has preserved much of the foundation laid by Ocarina of Time over 15 years ago, which happens to be the best selling game in the franchise; that said, that's more of a constraint for the story and not the actual gameplay.
I'm not sure how well this idea would work out, but what if Nintendo toyed with the ideas of various subseries like other well established franchises including Mega Man do? Nintendo could periodically revisit a certain style of game to please fans who prefer that direction. This could be used to return to the very start of the series creating 8-bit adventures similar to the the original NES game and the Gameboy titles (returning to the Megaman example, this idea would be similar to Megaman 9 and 10 for that franchise). A Link Between Worlds was well received so a similar treatment could be used for the more modern top-down games started by A Link to the Past. It's a theoretically simple solution to establish some continuity in the franchise.
This will always be a conversation topic for Zelda players as Nintendo likes to throw a complete curveball every few years, and as you stated, the series creators constantly throw around the phrase that the next game will be a complete reinvention of the series. I won't go into too much detail about that nebulous claim here although I do believe that creating such standards of hype for upcoming games only causes frustration upon release. The last few Zelda games, especially, have been alienating to large portions of the fanbase.
The thing is, the constant critical success of the series gives the developers more leeway in taking risks and continuing to experiment with the defining characteristics of the Zelda formula so to speak. The commercial side of things is a bit blurrier since Nintendo has preserved much of the foundation laid by Ocarina of Time over 15 years ago, which happens to be the best selling game in the franchise; that said, that's more of a constraint for the story and not the actual gameplay.
I'm not sure how well this idea would work out, but what if Nintendo toyed with the ideas of various subseries like other well established franchises including Mega Man do? Nintendo could periodically revisit a certain style of game to please fans who prefer that direction. This could be used to return to the very start of the series creating 8-bit adventures similar to the the original NES game and the Gameboy titles (returning to the Megaman example, this idea would be similar to Megaman 9 and 10 for that franchise). A Link Between Worlds was well received so a similar treatment could be used for the more modern top-down games started by A Link to the Past. It's a theoretically simple solution to establish some continuity in the franchise.