My view is that it may appear to work for a few years with Yoshihide Suga, a harsh but fair (or fair but harsh, if you're a glass-half-full type of bureaucrat) taskmaster with ample experience communicating and working with a wide range of senior and not-so-senior officials, in charge. It won't matter in the long run, though, unless the parties in power stop relieving their cabinet and subcabinet political appointees every other year or even more frequently. Seriously, how can any minister (or his/her subcabinet apprentices) hope (or want) to impose his/her will on key policy issues when he/she knows (and knows that his subordinates
know) that he/she is only on that patch of the Earth for a short while? Actually, some do, with mixed results.

Makiko Tanaka secured the Foreign Ministry portfolio on the basis of her key role in drumming up grass-roots support for Junichiro Koizumi's upset victory over Ryutaro Hashimoto in the 2001 race for the LDP presidency (and perforce the prime minister's office) and little else by way of substantive qualifications, unless you count a visceral pro-China stance dating back to her days as her father's de facto first lady.
(She opted for MOFA over-METI, much to the relief of the officials there.) Many of her problems revolved around process and personalities, while clashes over substance rose over casual comments running counter to policies long established under the LDPO regime or (in the case of Yasukuni) the prime minister's own wishes.
Would Boss Coffee appoint Tommy Lee Jones as its CEO just because he helped it sell canned coffee?

Good. I didn't think you thought so. Next up, Shigeru Ishiba.

Ishiba must be the most qualified individual to be appointed Minister (or Secretary-General) of Defense in post-WW II Japan. Why, he breathes national security 24/7.at least when he's not inhaling fumes from the superglue that he uses to construct military vessels and aircraft from plastic model kits. Appointed as Minister of Defense in 2008-he had served in 2002-2004 as the Secretary-General of what was then the Defense Agency-in the wake of a series of scandals, he promptly instigated a series of reforms on which he put his personal stamp, reforms that received a mixed welcome from within MOD, which was probably a good sign.
Unfortunately for Ishiba, the 2009 election and the subsequent DPJ regime happened. The upper house DPJ pushed Toshimi Kitazawa for a cabinet post-possibly because Azuma Koshishi wanted to eliminate a rival-and Ishiba's institutional reform was stopped dead in its tracks.

Does anyone think that the appointment system really matter, if this process prevails? Or if if it doesn't?
If you do, I think that you're looking at the wrong end of the periscope.

I could go on and on, with other examples, if someone would pay me to do it. I also may write another post, just for the fun of it, from the senior bureaucrat's perspective. But enough for now; it is late, I am drunk, I need to put my mother to bed, and I've got to get my next fix of Zegapain (with a mildly interesting premise that has its roots in groundbreaking science fiction such as Ubik and "The Unpleasant Profession of Jonathan Hoag". (Count Job's ordeal from the Old Testament, if you wish. God, what a jerk.not Job, mind
you.)