The sheer size of the supply chain you need to create to make a working machine is massive. It's one of the reasons why ASML got ahead of the Japanese companies that tried to do everything in-house.[3][4]
It took 17+ years and €6 billion in R&D to get EUV working [5] (as such EUV litography became feasible in the 90s), so ASML's leading position on the market is justified. They have to recoup all the costs, so they will make sure to keep the market leadership through all legal means.
My guess is that if someone would come up with a more efficient EUV plasma generation or better optic systems, ASML would acquire the company and take over the technology.
Regarding the negotiating power, some companies like GlobalFoundries couldn't afford ASML's EUV machines, so they parked their EUV plans [6]. It's only big players like TSMC, Samsung and Intel that can afford this tech and all these companies know their worth and prices. ASML needs money to pay for the R&D and can't afford to lose it's biggest customers that are also buying their non-bleeding edge technologies (DUV litography).
I don't know the business side of things, but it's definitely going to be interesting to see what happens with competition in the EUV litography in the upcoming 10+ years.
EUV litography and silicon-based chips have their physical limits, so there might be other ways to continue improvements.[7]
[1] https://www.reuters.com/article/us-asml-holding-xtal-court-i...
[2] https://semiengineering.com/extending-euv-to-2nm-and-beyond/
[3] https://ideas.repec.org/p/eti/dpaper/05007.html
[4] https://youtu.be/SB8qIO6Ti_M?t=673
[5] https://www.asml.com/en/products/euv-lithography-systems
[6] https://www.anandtech.com/show/13277/globalfoundries-stops-a...
[7] https://semiengineering.com/making-chips-at-3nm-and-beyond/