I take on fully what you are saying above and am in no way promoting being sloppy with checks.
I understand what you're saying. Clients don't like to wait. I remember an influential banker we used to fly regularly who was known for climbing into the airplane and simply saying "go fast." That's what we did.
I worked for a Learjet operator who insisted that we be taxiing as soon as the engines were started, and that's actually a very common thing; usually the engines were being started as the clients were settling into their seats. Clearances already obtained, all necessary checklists up to that point performed, coffee and ice ready, newspapers laid out on the seats, clients expected a turnkey operation: show up and go. Fast.
I flew Piaggios for a thousand hours or so, and the same thing there. Not at all uncommon to leave the right engine running when dropping or picking up a passenger, circumstances depending. I flew ambulance in King Air's, Lears, and Senecas, and we did the same thing. Much of the time I had engines turning as the crew arrived to get into the airplane and we were moving as the door was closing. There was never a delay with patients at the airplane; everything was always ready. When I got a dispatch, the airplane was already preflighted, and during my drive to the hangar I briefed and filed over the phone. My preflights were often long, as was my preparation, but I did it at my leisure before a flight was necessary, always at the start of a shift, and as the day or night progressed. Even in those states, however, I did the full checklists and did them out loud, as a single pilot (it kept me honest in not skipping things, and it put the record of having done so on the cockpit voice recorder).
A lot of our operations in Afghanistan have tight slot times. The runways get used a lot, and to make it work for everyone, there are slot times for ramp space and airspace. At some locations they're very hard-line about it, too. One can be half-way through with unloading the airplane and be confronted with a ramp manager who will tell you point blank, "you have 20 minutes; at the end of those 20 minutes you're departing whether the airplane is off-loaded or not." Arriving late can be extraordinarily bad; imagine flying all the way there, only to have to take off and fly home with half of the load still on the airplane. Not good; one must be on time and work within the constraints that are given. Weather, traffic, and mechanical delays must be factored in.
As another poster here stated that in the military in the UK they are expected to learn the checks by memory and then have a checklist.
The military is very big on knowing the procedures, but it's really the same program at any airline, and any conventional training facility. Simuflite and Flight Safety do the same thing: flows, backed up by checklists. It's just good cockpit management, and whether one is on the ground or in flight, performing the appropriate flows enables one to keep focused on the airplane and the environment and stay alert, while still accomplishing everything that needs to be done, backed up by a checklist. It's the same practice that I teach a student in a light, single engine airplane. In normal use, the checklist is a confirmation tool, not a do-list. Only in abnormal and emergency operations does that switch around.