I'm rather confused at the prior statements. Are you advocating against dive planning? Every training agency, whether Tech or Rec focused advocates creating a dive plan and diving the plan. I don't understand how having a dive plan translates into an inability to making real-time/on-the-fly modifications. That's a lack of a experience in planning dives and executing dives. Maybe it's just me but I find the OP's following statement contrary to what I have been taught by NAUI, PADI or GUE.
"With the computer, it feels like I am safe to dive without any plan whatsoever, other than making sure not to incur deco."
How many dive professionals will advocate this to their new students. How many of you, who are dive professionals, can state that such a statement is in-line with your agency's teachings? There is a HUGE difference in using a dive computer to verify/corroborate the validity of a dive plan and using a dive computer to blindly tell you when you're in deco and your dive deco profile during the dive. Every dive computer that I have owned, beginning with my old Oceanic Prodigy, has a dive planning function. It's something that needs to be done on every dive. Some dive profiles require rigorous calculations and preparations, others do not. A dive to 30ft with an AL80 doesn't require as much planning as a dive to 200ft with two deco gasses. Can you modify either dive on-the-fly? Absolutely! Can you modify the second dive profile as much as the first dive? Probably not...