I agree with this, and I think this kind of effect should be extended to all shield + buff combos. Generally, shields are made so that players are incentivized to attack them (Sion's W is a good example), and making a buff purely conditional upon the uptime of a shield is one of the best ways of doing that. Janna's bonus AD, Naut's on-hit effect, Skarner's bonus movement speed and Urgot's slow are all great examples of buffs specifically tied to their shields, and the fact that some on-shield buffs are completely independent from the shield itself does not make for good consistency at all.
There might be a concern that this would be a nerf to the affected champions (and it would be), but the advantage to a change like this is that it would make those champions healthier, and would allow them to receive more power elsewhere. Lulu, for example, could definitely use some slightly softer mana costs, and Ivern could perhaps have some better-tailored interactions with his passive and specific jungle camps (he shouldn't really have to spend health on the scuttle crab, for example). I'd much rather see a champion's power be redistributed in a healthier way than kept as is, simply because they're balanced in their current, less healthy state (though Ivern himself likely just needs a straight-up nerf).