But with the universal DH almost certainly about to be added to the National League, the Mets should have an extra spot to play with. Canha could DH often if the Mets sign Suzuki, or they can use a rotation at DH.
It should also be noted that Nimmo, whom the Mets are interested in extending but who recently hired Scott Boras to represent him, is a free agent after the 2022 season. So the Mets might need an outfielder sooner rather than later.
The presence of J.D. Davis and Dominic Smith on the roster could complicate things a bit in the event that the Mets sign Suzuki, but two players who might not have a future in New York (Davis, Smith, and Jeff McNeil are all available via trade) should not prevent the Mets from going after Suzuki.
As far as cost, MLB Trade Rumors predicted that Suzuki would get a deal worth $55 million over five years.
It is true that Steve Cohen's Mets can afford to do anything they want, but it's also true that Cohen (and every other owner in the sport) will not spend blindly forever. The Mets can exceed the luxury tax in 2022 (and will probably also do so in 2023 and 2024), but they will likely want to get back under it by 2025.
So cost does matter, and it's something that could make Suzuki more appealing than someone like Bryant (the versatile Bryant still makes lots of sense regardless), who could get a deal worth well over $100 million.