Why doesn't `\d` work in regular expressions in sed?

\d is a switch not a regular expression macro. If you want to use some predefined "constant" instead of [0-9] expression just try run this code:

s/[[:digit:]]+//g

There is no such special character group in sed. You will have to use [0-9].

In GNU sed, \d introduces a decimal character code of one to three digits in the range 0-255. As indicated in this comment.