I think there would be a weird sort of symmetry with HM The King removing the HRH from Archie and Lilibet.
Unless I'm mistaken, the last time British titles were outright stripped from British Royal Family members (rather than just not given) was when several members had German sympathies (due to being German) while England was at war with them. They were seen as betraying England in a similar way that the Sussexes have constantly been accused of betraying the very foundation of the British Royal Family. Stripping Archie and Lilibet of their titles would be a blatant way to show that they, by association with their parents, betray the ideals that the BRF strive to keep, similar to their German enemy-of-war cousins.
Sure, HM The King could go the Lady Louise/Viscount Severn route where Archie and Lilibet have the styling HRH Prince and Princess yet never use it, since that would leave the same amount of people using HRH as before rather than increase it, but that wouldn't go far enough to punish The Sussexes for speaking out against the BRF as much as removing their titles would. No, Archie and Lilibet should experience the same fate as their distant cousins who actively fought against England.