The talent and even many of the ideas came from NASA and old space, while SpaceX has both inspired and created a generation of it, there was always strong engineering talent in rocket science.
The primary issue for other companies is culture and institutional ability to foster innovation and take risk.
The old space organizations like ULA or Boeing et al and government funded are extremely risk averse and are also optimized for other priorities like having presence in as many states as possible or using old designs/ components to keep jobs funded and so on which limits them.
The new space companies do not have the resources to be as aggressive or fast although they are trying, they do not have free cash flow of SpaceX or extremely wealth and committed sponsor. Blue Origin+Amazon(Kuiper is theirs not BO) have resources but are not fast or aggressive and most likely chance to compete if they can get their culture sorted.
Private rocket companies were not successful businesses before SpaceX for a reason, its success has inspired capital inflows but problems are the same.
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Astra, Rocket Labs, Relativity and Firefly are the only ones with some track record of orbital launching vehicles, Astra went private at 99% down round for just 11M in March-24 and are probably going to be either acquired or shutdown.
Firefly has no immediate reuse plans. Terran R and Neutron are the realistic contenders for reusable vehicles if successful(big IF) then will have Falcon 9 equivalent competitor commercially available by end of the decade (13 years after Falcon 9 landed regularly in 2017). Starship will be active well before 2030 and be a generation ahead again. SpaceX when Starship launches commercially say in 2025 are at least 20 years ahead of everyone else and currently 10 years ahead with Falcon 9.
The last time space industry had this kind of disparity were the few years after Sputnik and other soviet first launches, to catch up the federal government spent multiple % of GDP and made it the national priority and employed 400,000 people to do it. SpaceX is not Soviet Russia it is a domestic company NASA and Space Force benefits from and Trump/Biden are not Kennedy so that is not going to repeat.
Realistically next 40-50 years will be dominated by SpaceX in both satellites and rocket vehicles, even if they stop innovating soon.