Why don't deep wrinkles respond to peels?

One source names deep wrinkles as a poor fit for peels. Read its exact words before you plan anything.
The line to start from
my.clevelandclinic.org lists what does not respond well: "Sags, bulges, deep scars, deep facial lines and more severe wrinkles don’t respond well to chemical peels."
Reading it as a directive
Do not expect a peel to fix deep facial lines or more severe wrinkles. The same sentence puts sags, bulges and deep scars in the same group, so check whether your concern is one of those too.
Steps to take
- Note which lines on your face are deep and which are fine.
- Ask your provider whether each one counts as a deep facial line or a more severe wrinkle.
- Ask what they would offer for the lines a peel is not suited to.
- Read the full list of peel types and conditions treated in the Chemical Peels overview from my.clevelandclinic.org before the visit.
A longer view of peel research
A review of evidence and considerations for chemical peels in skin disorders and aesthetic resurfacing gives a longer view of what peels are used for. A split-face study of trichloroacetic acid and phenol spot peels for freckles is a narrower example of a peel study.
If your provider’s answer is unclear
When you meet a provider near Saline, Michigan, ask them to explain in one sentence why a peel suits or does not suit your deepest lines. If the sentence is vague, ask again.