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The phrase “infinite list of” is correct and usable in written English
You can use it to describe an endless number of items or choices. For example, “The menu at the restaurant had an infinite list of delicious dishes.”
Exact(17)
"Everybody's assuming there's an infinite list of people waiting for a spot to garden," Ms. Stone said.
But what was created was a capability without a constraint, and a new infinite list of foreign targets to eavesdrop on, no matter how marginal the advantage gained, as the 2009 Turkish GCHQ brief demonstrates.
If the names on the infinite list of available fish are baffling – mero, lecha, breca, zama – refer to illustrations at the back of the menu or opt for the surtido, the mix.
With the disdain he holds for many of his peers (he has declared other indie bands to be "boring and stupid" and "fucking babies, they want their diapers changing") and his seemingly infinite list of pre-rock'n'roll influences (from Henrik Ibsen to Disney's Fantasia), Cox clearly sees himself as indie-rock's last great outsider.
The Lewises note that this strands us with an infinite list of primitive terms.
What would satisfy 'Jones believes the earth is round' is an open-ended (infinite) list of inferrings, imaginings, saying, and doings (etc).
Similar(43)
On the other hand, one may wish to avoid a quasi-infinite list of body representations.
All apps available for use with the iDrive system, no matter the platform, must be "optimized for safe use" while driving (e.g. not requiring the driver to take his eyes off the road to scroll through a near-infinite list of songs), according to the press release.
(In reconciling the finite with the infinite, bear in mind that if we list all the natural numbers 0, 1, 2, … in order, we obtain an infinite list every member of which is only finitely far from the beginning, and also has a well-defined predecessor and successor.
To exhaustively describe M in terms of first-order sentences, we need an infinite list ⟨li : i < ω⟩ of literals, where li := Pci, if di ∈ PM, and li := ¬Pci, if di ∉ >PM.
These are just a few examples of a practically infinite list.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com