I'll take a shot at this. Before I do, I will caveat everything by saying I think Boeing's approach to heading bug logic is extremely flawed and I share your frustration with this tedious routine we follow as we fly. My frustration lies in the poor design of the system. However, I do feel that the technique of matching the bug is a necessary evil for a few reasons. I've flown four Boeings (737, 757, 767 and currently fly the 777). I've also flown the A320 and the MD-11.
Without getting unnecessarily aircraft specific, I'll just say that there are far better ways to skin this cat and the heading select logic found in other aircraft is vastly superior in my opinion. As you mentioned, the logic includes removal of the bug when not in use. Some systems also can "remember" which direction the heading knob was turned prior to actually engaging the heading mode. In addition, some systems put the heading bug in a dormant state once the aircraft has captured the selected heading. By this I mean it's not always "hot" like on a Boeing and turning the knob to a new heading will not create an immediate turn. The button must be actuated again to begin the turn.
I offer this info only to illustrate that someone's background in other aircraft can set up the potential for errors when "muscle memory" and former habits potentially surface at the wrong time during high workload situations. So having everyone start on the same page and keep them on that page when things get busy has huge value in my opinion. Also, FWIW, matching the bug to current heading is procedure at FedEx and was at United when I worked there - not sure about now. You may not be able to find that specifically addressed in your books but I would argue that's it pretty much procedural with most Boeing operators whether they put it in print or not.
So, one of the big reasons we do this is standardization. We successfully put two (or more) pilots who've potentially never flown together and only met an hour or two prior together on flights routinely. A major reason this happens uneventfully every day is standardization.
You didn't care about the U2 heading bug at times and at others you chose to do something with it you found helpful. In a single seat aircraft you have that luxury since your techniques and opinions are the only ones that matter. At "brand-X" you don't have the same leeway without creating the potential for confusion.
I'm not trying to make matching the bug to your heading a bigger deal than it really is, but not doing it can lead to other issues - some big, some small. Maybe it's in the sim or out on the line, but depending on who you're crewed with, what seems like a little thing can turn into something big in rapid fashion.
While we all know assumptions are bad and making mode changes without verifying the variables is bad technique, I'm sure you've seen someone just reach up and push the heading knob when ATC clears you to "maintain present heading". Their assumption is the bug is matched - which at many airlines is a valid assumption since it's procedural (not excusing not checking first - but we are dealing with fallible humans). So, you get rushed and give the jet to the other guy in the descent so you can load and brief the approach. Today, you left the bug "over your shoulder" and it's not even visible on the ND. So, he attempts to comply with ATC's instructions and assumes the bug was matched. When the unexpected turn starts, he realizes it isn't and now has to recover. Recovery techniques are going to vary from rapidly dialing in your old current heading (if he remembers), using heading hold, going back to LNAV momentarily, etc. That doesn't even account for the startle factor which will vary based on proficiency level, fatigue, distraction, etc. and may delay the recovery attempt while he tries to figure out what happened. The bottom line is, a matched bug or even something close is going to be more forgiving of bad technique and avoid potentially bigger issues. On a side note - I highly recommend using "Heading Hold" when complying with "maintain present heading" for this very reason (technique only).
Since your technique means the heading bug could be anywhere at any time prior to you using heading select, by definition, you have to select something you want with the MCP knob before you engage Heading Select ("center the bug before you mash down" as you put it). On the other hand, those who match the bug can immediately engage Heading Select and then turn the knob to the desired heading. That distinction is important. Since your technique involves an extra step, EVERY TIME you use Heading Select, that's something the pilot monitoring has to be looking for as well. Since it's non-standard, that's going incumbent on you to make sure he's aware that needs to be in his cross-check. For example, ATC gives you a 220 degree heading change "the long way around" to the right. Any heading selected on the left of your compass rose when the button is pushed is going to command a turn to the left. So, are you going to dial in your current heading, THEN engage Heading Select and then command the turn to the right? Every time?... no matter what? Would it ever be possible (habit, task saturated, fatigue, etc) you might first select the desired heading and then engage heading select commanding a left turn you would then need to reverse?
I'd guess it's unlikely these issues are going become life or death matters. If they snowball thanks to a really bad day or just Murphy's law, they could still turn ugly with the FAA. Is it really worth any issues arising because you want to make a point? Most likely your airline pays you a pretty good bit of money to fly their jets and they want them flown their way. Why not make it easy on yourself and your crew members and play along?