No, actually, this sounds quite realistic and in many cases even reasonable. Medical insurance does this literally all the time. Insurance companies of many different kinds in general have to do this to prevent fraud and keep costs (and by extension premiums) low.
> There is no fixed path when modernizing a complex legacy system. There is no rulebook to follow.
Of course not. But as an engineer tasked with this kind of project your estimate should reflect some kind of plan for accomplishing the project, where the plan has more concrete and actionable steps that make estimation easier. And if you are good at your job, your estimate should account for known-unknowns (eg this part is contingent on something partially out of our control and may be delayed by X months) and give enough slack to handle inevitable unknown-unknowns without excessive padding. And uncertainty regarding any particular risks or variance in how long somethign takes should be explicitly noted and communicated.
My $0.02:
The unfixable estimate vs deadline problem ultimately boils down to money. A particular project might be worth it if it ties up 10 people for 3 months, but not worth it if it ties up 10 people for 12 months. And relatedly, businesses oftentimes find themselves needing something finished by a certain time to close a sale/keep a customer happy/catch up to a competitor, and the stakeholders on the other end (customers, investors, partners) need some kind of date for their own planning.
Good estimation is really about identifying the probability distribution of the completion date, rather than a single "expected" completion date, and identifying/communicating the related risks. For a big project this itself probably will take a few days to months to complete and communicate. If you do this properly, there should never be any ambiguity as to what is an estimate and what is a deadline. If you don't do this, you are basically assuming that your manager (and their managers and so on) can read your mind and have the exact same understanding as you do regarding how firm the estimate is + what the risks and possibly "actual completion times" are. You're also denying them the opportunity to help you derisk or accelerate the project by eg adding more people to work on it, reach out to some external stakeholders, or communicating the end date to eg investors/customers in a way that reflects risks. You also need to update the people that care about the completion semi regularly to tell them about any new risks or known unknowns for the same reasons.
If you are wildly off with your estimate even after spending the time to breakdown the project with a more actionable plan, identify risks, and come up with ranges/a distribution of outcomes - let's say you blow past your p99 time to completion - you are probably just bad at your job (or trying to operate above your skill level) and it would probably be very reasonable for your manager to hold you to a deadline with the threat of firing you/canceling the project. Yes, the sunk cost fallacy dictates that even projects that run over should probably be completed in many cases (though since overall budget/personnel are usually constrained I think the opportunity cost of doing other things becomes pretty important). But if people can't trust you to estimate properly they probably can't trust you to lead a project or to have estimated the remaining time to finish the project.