It’s a common misconception that American accents have changed less than British accents. Both accents have changed. There’s a pretty obvious example that American accents have changed in the fact that many American accents have vowel mergers that result in pronunciation mergers of syllables with different spellings that aren’t merged in non-American accents. Wikipedia gives the example odd-facade-thawed, which all rhyme in most American accents but which have completely different sounds in non-American accents.

Likewise some American accents have lost the distinction between the vowels in marry-Mary-merry, or merge the vowels in pin-pen.

If American accents had changed less then why would they continue to use spellings that no longer match pronunciation in their own accents but which do match in many non-American accents?

The reality is that both accent groups have diverged.