I've learned mostly the opposite. Those that become indispensable rarely get promoted because moving them would create a huge gap in a necessary role. At best, these engineers are rewarded with 'pseudo promotions' like team lead or lead of two projects - with no pay increase or perks, just more people to manage, PowerPoints to create, weekly status meetings to attend, etc.

Playing politics, dressing better, getting in shape (opposite of the typical hoody-ed neck beard) and befriending those above you, while learning a little bit of lots of business facets, is the path to real promotions.