Now, if the Canon is so well calibrated/linearised, there seems to be less use for custom profiles for a specific printer.
As mentioned above, be careful not to mix up calibration (or linearization) with profiling. Calibration simply puts the printer into a known state for that paper / print settings. Ideally those results are repeatable within a narrow band but actual results probably vary. Calibration can depend on the paper, the print settings used (in HP land that's the "paper preset", plus any subsequent changes to the paper settings made by the user, such as ink load), changes in humidity, changes in printheads / health, etc. For these reasons periodic recalibration is required (HP prompts for it), and is mandatory before attempting any profiling.
Profiling on the other hand builds "translation" tables so your system can "speak colour" with your printer, so results are ideally consistent and predictable (soft-proofing). In theory the profile is good "forever", as long as you keep the printer in calibrated state. (In practice I reprofiled pretty much every time I recalibrated because HP makes it stupid easy to do.)
I don't think there's anything revolutionarily "new" here in the Canon 4600's calibration that you didn't already have with HP. Maybe it can hold a bit tighter tolerance, but the marketing claim of "same results on any two printers anywhere" was also HP's almost 20 yrs before (tho ofc HP could also *profile* itself), so I think none of the considerations for profiling are really any different because of that. If you weren't already making your own profiles on your HP and you were happy with mfr ones, then it's probably the same with the Canon.
The choice to use a canned mfr profile vs your own is a personal one. The variables above are some of the reasons why a mfr profile might not always be the "best" fit for your situation (but "best" is a personal judgment too). And if you want to adjust print settings such as ink load then you pretty much "need" your own profile (unless again the differences don't bother you). But you can also just use a mfr profile and if you're happy with the results then just move on in life. Again HP made profiling so easy that there was no reason not to make our own (and when I compared results, I found some of HP's canned profiles were poor or at least very conservative).
As for using your HP's built-in spectro to profile the Canon, yes you can do that and I think one of the many PDFs/manuals from HP's site explains how. If you have an HP Z3200ps then I recall you choose a profile target image in the HP Colour Centre, then print it on your Canon, and then use HP Colour Centre again to scan it with the HP. You then get an output file that you need to take into another (non-HP) software to create the profile for your Canon, whether that's Argyll or whatever. The hows and whats of that depends on the specific software.
Edit: as someone here mentioned recently, there's also some "overhead" costs/effort/space associated with keeping an HP Z-series operating solely for use as an occasional profiling scanner.