I don’t use different color profiles for web and print. Human vision is very adaptable to different whitepoints. I use a 27" monitor, which allows me to have a fair amount of neutral frame (e.g. grey tool palettes) around my pictures when editing, so it doesn’t matter too much, which specific whitepoint I use. Read-on below for my explanation why, with the disclaimer that I’m just a physicist by education but by no means a color management expert.
BUT, my point earlier was that once you have some reasonable color management in place, irrespective of white point, you actually should pay attention to image contrast next, because it will have a vastly bigger impact on your prints than subtleties, which potentially are addressed by profiles with different whitepoints. Managing contrast includes handling gamut limits in bright areas. A convincing sunset ‘sky on fire’ is a lot more difficult to create in print than on screen, due to the limited contrast and the saturation limits that go along with it.
Back to color profiles, the rationale for 6500K for web editing is likely that that’s close to most screens native (=brightest) white point, similar to overcast daylight. Therefore, you’ll have a similar viewing impression as many others, when you ignore the influence of the current viewing environment. If you use a 6500K profile in a room lit with popular (here in Germany) 2700K ‘warm’ household lamps, your screen will look blueish, not white, unless it fills a really large portion of your field-of-view. So probably your edits will end up with a rather warm touch. On a small screen, a dark room will, while maybe color-balance wise OK, on the other hand lead to rather dark edits, unless there is a lot of tonal ‘reference’ material placed on the screen around it. Editing in a room with daylight would likely result in more balanced edits as long as it isn’t too bright.
Editing for printing is basically no different than for web use, when it comes to color balance. I have successfully edited a lot of pictures for printing with my monitor’s native white point (close to 6500K). Color profiles take care of mapping colors in the reference color space (CIE, modeling the average human color perception) to a specified viewing condition, including different white points. This allows to transform color values between them, which will then emit the best matching (according to the rendering intent) stimulus, achieving the closest color perception despite the different viewing conditions.
The major difference arises when you actually look at prints, which are lit by some defined light spectrum, to check them or a color chart or picture for reference in the same environment as you use your monitor for pictures on-screen. Then you do need to match those reflective and emissive viewing conditions simultaneously as closely as possible, so that they generate consistent stimulus. This is where e.g. D50 lamps, color neutral booths, and screen profiles with matching white points and brightness come into play. If you print yourself, it may be worthwhile to create a screen profile closely matching your print viewing conditions, otherwise taking your ‘average’ working environment approximately into account should be sufficient.