I think the OP (and me too) are looking for a compact, portable device that does show by itself components curves.
there are already aout there lots of octopus and bulky component testers...
Yes, that's the idea. I am really tempted to build something... I like the idea of keeping this minimalistic, with just a small touch display, power button, USB charging port, and two jacks for test leads.
Does a 3.2" touch screen (320*240 pixels) sound large enough? It would only be used for qualitative "eyeballing" of curves, but should be able to display labels on the voltage axis and let you estimate diode forward and breakdown voltages.
One can always get fancy in the software, trying to recognize certain components and display rough measurement values for them. Minimal controls would be the selection of two to three voltage ranges, I'd guess: +-12V to check most diode voltages of interest, +-2V or less to avoid damaging sensitive circuits -- anything else? Are different current measurement ranges required, or different frequencies for capacitor measurements?