No, it wasn't. This is more like a Dr. Jekyll and Mr. Hyde story where two different philosophies clashed repeatedly.
The GameCube was a response to the underwhelming sales of the Nintendo 64 where Nintendo focused on getting more third party support. They succeeded at that, but ended up selling even fewer consoles than before. The GBA connectivity was more or less a desperate attempt to differentiate themselves from PS2 and Xbox by leveraging their dominance of the handheld market, but the idea didn't gain any traction.
With the Wii Nintendo went back to the drawing board and looked at the NES for inspiration. What they came up with was so ass-backwards from what they were supposed to do according to conventional wisdom that it was declared that Wii would be Nintendo's last console. Wii isn't a continuation of the GameCube, but that's exactly what made it so successful.
The Wii U was Miyamoto taking the reins and reviving his beloved GameCube. In Iwata Asks, Miyamoto repeatedly says things along the lines of "the marketing was at fault". Miyamoto seriously believed that the GameCube was correct and only happened to be a victim of unfortunate circumstances. You are absolutely correct that Wii U picks up core ideas of the GameCube, but Wii U was never meant to be a stop gap console. Nintendo expected it to be as successful as Wii at least. Wii U solely existed because of Miyamoto's desire and his belief that the GC was great, and being able to convince the board of directors of this mindset. The same holds true for the Nintendo 3DS; Iwata Asks has Iwata laughing after saying that Nintendo has always failed when they tried 3D stuff, but this time it had to be the right time for 3D.
The first thing Nintendo did with Switch was to remove Miyamoto from the design process. Just like Wii was a rejection of the GC direction, so is Switch a rejection of Wii U. Switch isn't a two-screen console. When Nintendo talked about NX, they made it clear that a drastic change would be coming, and Switch is really nothing like Wii U.
It is correct to say that Switch is deliberate and was carefully planned, but the console is not the result of a roadmap that Nintendo conceived in the early 2000s. It's the consequence of a different design philosophy completely and utterly failing. If this had been planned all along, then Miyamoto would have maintained his position in the company, but he's been put in a better form of retirement.