The only exception that comes to mind is scanning. Cannot say, myself, but have heard others claim that uninstalling in entirety left them shortchanged on some scanning functions, and wish i had clarification whether Apple or third-party -issued drivers and apps suffice. I have found some utility in the "HP Scan.app," per se [e.g. batch/bulk feed, w/ stored presets, etc. on the 8600]. But said app is right there in front of me. I can use it or leave it alone. I know where it resides. I can readily interrupt it, as with any other proper app.
The horror is crap that malfunctions, can be identified by name, and cannot be located with OS X Spotlight or any other reasonable means,.
What I will say to anyone seeking assistance with HP printers in OS X is this –– by all means, steer clear of HP Support Forums. I say this not out of hatred or animosity. Simply pragmatism. Your odds of gaining correct guidance there are worse than the 5,000:1 odds posted this year against Leicester winning the Premier Football League championship. Just statistical objectivity. On second thought, I guess Leicester proves that you might find a solution from HP, but London bookies still gave even better odds that Elvis would be found alive in 2016, so go ahead and look.
The worst offenders there are HP employees. I utterly admonish their manner, e.g. posting "solutions" which are, even by their own admission, untested, unknown and, by definition, unreliable, dangerous, counterproductive––in a word, worthless. They thus offer advice which is utterly wrong, apart from describing, with precision, the method for us to formally congratulate them in the forum.
One must treat HP as a hardware manufacturer, alone [which they do, frankly, quite well]. They do not understand the service sector. They cannot assist users with operational services. Above all, they know not OS X.
The moral of the story: HP is simply, and horribly misguided. Their employees post crap. [But don't say so on their forum––I've seen moderators rebuke complaints in like language, when the complainant was fully correct that a particular piece of HP advice was manifestly hokum.] This is not their individual fault. It is, in fact, a testament to the perfection of HP's trainig process. One will note that they post crap with perfect uniformity. This is sad, but it just is so. Their training must be improved.
While we're analyzing London bookmaker bets, case in point –– I'll offer 200:1 to anyone who can, utilizing all search-engine spiffiness you care for, or whatever, even knowing what you now know, find this solution on an HP Support Forum, within the past ten years' postings, apart from the mention I there made today, referring people to the above solution offered by 13orPkooBcaM.