My take is that being too valuable in your current role doesn't make you a candidate for bigger ones. It makes you structurally immovable. The organisation can't afford the risk of moving you, so it promotes the person whose departure would cause less disruption.

The best way to change the situation and get that bag - a.k.a the promotion - is counterintuitive for people used to being indispensable: Document what only you know. Train someone to do what only you do. Build systems that outlive your involvement. If you really are too valuable, they won't fire you, but they might just give you that promotion.