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The phrase "eat into" is correct and can be used in written English.
This phrase is used to mean "to gradually reduce something over time". For example, "The high costs of living are slowly eating into my savings."
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Delays eat into servicers' margins.
Expenses eat into returns.
More important, they eat into time.
Anything less would eat into their capital.
That would eat into its thin profit margins.
Labour will probably eat into the SNP lead a bit.
It's whether you eat into your opponent's real-estate portfolio.
This is expected to eat into the critical export business.
But will rookie Perine eventually eat into his carries?
This can eat into per-call savings quickly.
"It does eat into your existence," he said.
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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