That's why red+blue=purple feels a bit like violet. It creates a similar double firing.
(And why red plus green gives an even more accurate yellow. The long and medium cones have a lot of overlap.)
I think the misconception comes from plots of XYZ color matching functions[3]. The X color matching function indeed has a local maximum in the short wavelengths, but X doesn't represent L cone stimulation; it's a mathematically derived curve used to define the XYZ color space, which is a linear transform of LMS color space selected for useful mathematical properties.
[1]: https://en.wikipedia.org/wiki/LMS_color_space#/media/File:Co...
[2]: http://www.cvrl.org/
[3]: https://en.wikipedia.org/wiki/CIE_1931_color_space#/media/Fi...
Second, the term imaginary color already exists, and it refers to a specific thing [0], and the colors on the line of purple are not one of them. What you are describing is a non-spectral color. They exist in day to day life and in nature, they simply do not have an associated wavelength.