Revert "Fix issue where DevTools would not be immediately available when using --start-paused" (#128117)

Reverts flutter/flutter#126698

There are a bunch of tool crashes on CI that start with this commit. I'm
not sure this PR is the cause because there is no backtrace from the
tool on the crashes. The only error message is `Oops; flutter has exited
unexpectedly: "Null check operator used on a null value`.