Accessibility usually enters a project as an audit near the end, producing a list of contrast failures and missing labels that get fixed under time pressure. The result passes, and the underlying interface remains difficult to use for the people the standard exists to protect.
The framing is the problem. Accessibility treated as a checklist is a cost. Treated as a design constraint, it is one of the most reliable proxies for interface quality there is.
The constraints are clarifying
An interface that works with a keyboard has a coherent focus order, which means its structure is logical. One that works with a screen reader has meaningful headings and labels, which means its content hierarchy is real rather than visual. One that meets contrast requirements is legible in sunlight, on a cheap monitor, and to the very large number of people with ordinary uncorrected vision.
Every one of those constraints improves the experience for users who were never the stated beneficiary.
Retrofitting is expensive because it is structural
Most serious accessibility problems are not styling issues. They are consequences of markup: a control built from a div, a modal that does not trap focus, a form whose errors are announced to nobody. Fixing those late means rebuilding components, which is why late accessibility work is so often reduced to the cosmetic subset.
Deciding at design time that a button is a button removes an entire category of remediation before it exists.
Automated tools find a minority of issues
Automated checks catch perhaps a third of real problems, and they are the easy third. No tool can tell you that the alternative text is technically present but useless, or that the focus order jumps around the page in a way that makes a form unusable.
A keyboard-only pass through the primary flows takes ten minutes and finds more than any scanner. Doing it during development, rather than during an audit, is the entire difference.
It correlates with everything else
Semantic markup is better for search engines. Clear focus states help every user under load. Text that survives magnification survives translation. The practices overlap so consistently that accessibility work is rarely wasted, even when judged purely commercially.
The legal argument for accessibility is real and it is not the interesting one. The interesting one is that the constraints make you build the thing properly.