I think this idea of having Nintendo's high-quality software on more technically superior hardware looks great on paper, but I think it really depends on the details of how the two came to work together.
In this scenario, has Nintendo become a Sony first/second party? If that's the case, I think the differing business philosophies would hold this union back more than anything else. I think Nintendo has received a lot of flack over the past two gens for releasing relatively underpowered devices, but I think a big reason for this to remain relatively accessible to consumers, and unique in a changing market. If Nintendo's parent company continued to produce $400+ console hardware and forcing its fans to pay for online-play, I don't foresee a big portion of its userbase jumping on right away.
There's also the factor if the developers themselves would be affected by the different business philosophies. Currently, Nintendo is essentially run by current and former game developers, which I suppose has its downsides as well as its advantages. I've read an interview in the past, where Iwata adamantly stated that he didn't believe Nintendo's developers would be able to perform their jobs as well if there was a risk of being laid off in the future. Would being run by a more convential board of business directors affect how Nintendo's developers performed their jobs? Would Sony's board of directors be willing to take salary cuts if this system floundered, or would they subject the entire division to layoffs?
Or is it that Sony sold the Playstation brand/division to Nintendo? If it's this case, I don't see why Nintendo would necessarily adopt the high-end hardware model Sony applies to its consoles. It would be interesting if Nintendo built a 3rd pillar console to go along with its handheld and new Wii iteration, though there'd always be the chance that Nintendo would kill one model early if the other took off, much like with the Game Boy Advance.
The only other option I see is if the two somehow formed a truly 50/50 partnership, which I believe is what OP is implying in the first place. If Nintendo was able to remain autonomous, and fans were still able to obtain the devices they enjoy at a reasonable price, then I see no reason not to support this. I just think the simplistic "Nintendo software + Sony hardware" that pervades the internet isn't really as simple as some fans like to pretend.
NNID: Zephyr25 / PSN: Zephyr--25 / Switch: SW-4450-3680-7334