I'm starting to think you aren't reading my posts... I'm not saying the lost health isn't significant(as I said it would roughly be 6% less and a change of 5% is sgnificant), I'm saying you have the gold to make up for the lost stats since bami's also costs less.
Current patch 1500 gold: bami+boots+100 gold left over. Pbe 1500 gold: bami+ruby crystal+boots. But pbe player gets 70 more health, and 50% more damage to minions with bami's(gold value of health: 186, gold value of bami's passive buff*: 166 gold, for a total gold value of 352) which is worth more than the leftover 100 gold you would currently have. So if you wait till you have enough gold to buy a ruby crystal and a bami's cinder(without sacrificing the things you already wanted to buy, like boots in my example), you end up with a higher gold value item build.
*Current bami's health value is 280= 746.66 gold value(based off ruby crystal), total price is 1100 gold, passive value is then 1100-746.66 = 353.33 gold. Passive value was doubled against minons for pbe, but not champions, so 50% increase in value of passive. New passive value is 530 gold. Pbe bami's health value is 200= 533.33 gold(based off ruby crystal), total price is 900 gold, passive value is then 900 - 533.33 = 366.66 gold. But new passive compared to old passive is: 533.33 - 366.66 = 166.66 gold value increase that isn't in the price already.