env and printenv are both external commands i.e. executable files, not bash builtins.
The problem with them is that some environment variables (such as _, and I also wonder if there are more) which they output don’t belong to the shell which invokes them, see here.
The yash shell has a printf built-in, according to its manual.
Some commands are provided as both builtins and external utilities. Take echo for example. On my machine (macOS) running Bash 3.2,
eval and exec are both built in commands of bash(1) that execute commands.
Consider this from the documentation of Bash’ builtin exec: