You'll still be glad you asked up front, because that kind of BS tells you something about the company. Sure you wasted your time in the interviews, but you now know not to push back on their initial offer because you don't want to work for a company that'd pull that on you.

The sunk cost goes both ways. The company has likewise spent a lot of time and effort interviewing you and if they are extending you an offer and you say no, the process starts over for them.

Especially if you have a job already, when they want to hire you is when you have the maximum leverage.

That's only when most of the interviews aren't automated via codility and similar atrocities. If they built or contracted a process that is scalable, interviewing you will cost them like $5 and almost no time outside maybe the final call with your future boss whereas you'll waste a lot of time.