Note that I'm not a professional and even am moderately color blind for some colors, so take my word for experience only

I am using a NEC EA231WMI "pre-calibrated" monitor, I guess yours functions the same or even better. I had bought the Datacolor Spider as well and my opinion is that it's only really useful if you print your own photos and you need to be sure your printer does what you want.
Now I print my photos at a professional lab, so the results are at least 99% reliable. With the Spider the colors where very good, but not noticeably better than the method I use now. I have sold the Spider a few years back already.
I have printed a select amount of images that I have saved on my pc. I compare them to my display and adjust contrast and brightness while doing so using the pre-calibrated RGB settings from the display. This and looking good at the histogram have given me a very reliable color result when printing photos.

My two cents is that the color calibration tools are definitely working, but personally I think you don't "need" them, but again I'm not making a living out of it. Also comparing to your smartphone isn't the best comparison, colors and contrast always look much more intense on smaller screens. The colors on the back of your camera also look more saturated and contrasty than the photo on your display. I think the most important thing is that the customers see the same or pretty much the same as you do. So check your images on your tv or other media to see if you like how they look there.

Bottom line, I took some photos of my cousins and sent them to my sister. My sister printed them at a cheap lab, but when I looked at the results they were pretty much how I intended them to be, so I'm happy.