What advantage does _Bool give?
The value of a _Bool is either 0  or 1. Nothing else, unlike an int.
 
Conversion to a _Bool always converts non-zero to 1 and only 0 to 0.
 
When any scalar value is converted to _Bool, the result is 0 if the value compares equal to 0; otherwise, the result is 1.
Examples:
#include <math.h>
#include <stdlib.h>
_Bool all_false[] = { 0, 0.0, -0.0, NULL };
_Bool all_true[] = { 13, 0.1, 42.0, "Hello", NAN };
Notice the difference of conversion/casting to int vs; _Bool:  (int) 0.1 --> 0, yet (_Bool) 0.1 --> 1.
Notice the difference of conversion/casting to unsigned vs; _Bool:  (unsigned) 0x100000000 --> 0, yet (_Bool) 0x100000000 --> 1.
_Bool adds clarity to boolean operations.
 
_Bool is a distinctive type from int, char, etc. when used with _Generic.
 
Prior to C99, C lacked _Bool.  Much early code formed their own types bool, Bool, boolean, bool8, bool_t, ....  Creating a new type _Bool brought uniformity to this common, yet non-uniform practice. <stdbool.h> is available to use bool, true, false.  This allows older code, which does not include <stdbool.h> to not break, yet newer code to use cleaner names.
 
OP's example with "doesn't enforce that a value is true/false or 1/0" does enforce that bools[2] had a value of 1.  It did not enforce that the initializer of 'c', an int, had to be in the range of [0...1] nor of type _Bool, much like int x = 12.345; is allowed.  In both cases, a conversion occurred.  Although the 2nd often generates a warning.