I entirely support the OP's suggestion.
Sure, Sephuz, Prydaz, and other multi-spec Legendaries HAVE USE in multiple specs, but that doesn't mean they're fun or change your playstyle. I also don't think anyone would prefer to have three all-spec Legendaries over having nine Legendaries (three per spec).
This system is designed to help people get Legendaries for their off-specs. There are plenty of people right now that have three all-spec Legendaries, and they would receive absolutely NO benefit from this change, whereas someone that has gotten three spec-specific Legendaries will get full benefit. There should NEVER be a point where getting a Legendary is a bad thing, but with this proposed system you are arguably punished for getting a utility all-spec Legendary as it diminishes the drop chance of all off-spec Legendaries. Unconditionally, a better system would be one that benefits all players instead of just some, and that's entirely setting aside Legendary balance.
I have no idea if anyone has already debunked this (I haven't read through the entire thread), but what you said isn't how it works.
Using the same system you described:
You have 100 BLP per spec
You play Blood and get Sephuz, and it costs 33 for each spec
You now have 67 in Blood, 67 in Frost, and 67in Unholy
You then get on Frost and get Drapes, and it costs 33 for each spec
You now have 34 in Blood, 34 in Frost, and 34 in Unholy
You now have Sephuz, Drapes, and Unholy Helm
Let's say you stay Frost and get Prydaz, and it costs 33 for each spec
You now have no BLP in any spec, but you only have 3 Legendaries.
While I do agree that this system is better than (or at least neutral with) what we have at this exact moment, the entire point of feedback is to improve potential systems, so saying that we shouldn't complain or discuss this proposed bad luck protection system, or that we're entitled for wanting something better, is completely asinine.
Someone that has no Legendaries will benefit from both Blizzard's proposed system as well as OP's suggested system. His definition of "rich" is someone with only spec-specific Legendaries (as they would gain the maximum benefit from this change), and his definition of "poor" is someone with only all-spec Legendaries (as they would gain zero benefit from this change). His choice of wording is a little bit off, but the concept remains.
What he said is not speculation; all-spec Legendaries are confirmed to count against your bad-luck protection for every spec it can drop for, so his scenario of someone having 9 Legendaries and someone else having only 3 is completely possible (and his suggestion would be helping the person with only 3).