Why do I get an error when deleting entries from Bash history?

The error is raised because xargs cannot find a history command. It is a shell builtin, as you can confirm with type history, thus not visible to xargs. Try

echo 1 | xargs history -d; echo $?

The return value is 127. In man xargs, EXIT STATUS section:

0 if it succeeds
123 if any invocation of the command exited with status 1-125
124 if the command exited with status 255
125 if the command is killed by a signal
126 if the command cannot be run
127 if the command is not found
1 if some other error occurred.

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Expanding on ilkkachu's comment, in principle you could invoke Bash and call history from the spawned shell.

echo 1 | xargs -I {} bash -c 'echo $HISTFILE; history' bash {}

The above command does not raise an error, after all the builtin history is available to the Bash shell. However, from that same command one also finds that HISTFILE is unset and history outputs nothing: The history is not enabled on a non-interactive shell. Again, you could activate it with the set builtin, export HISTFILE and HISTFILESIZE... But we don't want a headache. Editing .bash_history directly is the straightforward way to go.