Should Blue Sentinel give Health on Smite?

I rarely ever end up smiting blue, because gaining its buff will cover all my mana needs. The only time I typically smite it is if I'm giving the buff away and need mana, which is usually somewhat uncommon at that point in the game. Should it instead give health like Red Brambleback? The health gain on red often is what convinces me to start on red's side of the jungle. Plus, another health on smite may help the current "problem" with sustaining on the early clears.