Those Bloodnames are legal due to the Reaving rules. They are "cleansed" the moment they win the Reaving trial. That's nothing to do with pragmatism.
Not according to canon. It was an Annihilation, not a Reaving. The remaining Home Clans voted on it. (Page 150, TWoR)
Now, the Star Adders called a Reaving (Page 149, TWoR), but that got zero traction. The Annihilation vote is what stuck.
The Adders did not get their way, so they did not Annihilate the Steal Viper lines as would be proper ever since precedent set by the Wolverine Annihilation.
All of this aside, did you know the only Clan with a worse record of arming their lower castes than the Adders is the Blood Spirits? Yes, it can be argued that the Adders' lower castes arm themselves, but then the Adders' warriors make absolutely no moves to censure or punish their lower castes for violating Clan rules.
More pragmatic moves.
I think I missed something: which 5 Bloodnames and from which Clan?
Star Adders kept the following Annihilated Steel Viper lines: Grimani, Hoskins, Masters, Andrews, Breen, and Zalman. So actually it's 6 heritages. Only 3 of them were exclusive, but still , it's six more Bloodnames than should be kept since the Steel Vipers were Annihilated.
All this is on page 194 of TWoR.