Why doesn't `my $x = if (0) {1} else {2}` work?

In perl, $x = if (0) {1} else {2} does not work.

$ perl -E'$x = if (0) {1} else {2}'
syntax error at -e line 1, near "= if"
Execution of -e aborted due to compilation errors.

This makes sense, because if conditionals are not expressions in Perl. They're flow control.

But then

my $x = do { if (0) {1} else {2} };

Does work! How come a do BLOCK can accept an if conditional? But assignment can not? It would seem in the above the flow control must either

• know it's context in a do BLOCK
• always act as an expression, but have that syntax disallowed by the parser.

Moreover given the simple facts above, what is the right way to describe an if-conditional that behaves like that? Is it an expression with a value? Is it flow-control construct that has no value after evaluation?

And, lastly, what modifications would have to be made to assignment to have it accept an if condition like a do BLOCK.